I will devide the answer into two parts. The first part will be explanatory in nature, i.e. explain what the argument and its explicit premises are and where they come from. It is important to fully understand what you are dealing with and how the terms are used, and my understanding is that you are asking for an intelligible explanation of how someone would reason that way. Therefore, I think it is crucial to give you the context in terms of what validity means and how the premises are to be understood. The second part will try to address your criticism more directly and explain where the argument has problems.
Basically, your assumption "As far as we know, all the stuff (classically, matter or energy) has always been here in some form or another." is not as clear-cut as you seem to take it, but one step at a time.
Explaining the argument
The actual argument
I think the first step should be to formulate the argument in a form that is coherent. As per the corresponding SEP article already linked in another answer, a rather recent version of it by Craig is:
1 Everything that begins to exist has a cause of its existence.
2 The universe began to exist.
3 Therefore, the universe has a cause of its existence.
4 No scientific explanation (in terms of physical laws and initial conditions of the universe) can provide a causal account of the origin (very beginning) of the universe, since such are part of the universe.
5 Therefore, the cause must be personal (explanation is given in terms of a non-natural, personal agent).
On the form of the argument
The argument part 1-3 is a valid modus ponens, which just means that the conclusion does follow iff both premises are correct:
- For all x, if x at some point in time began to exist, x has a cause for its existence.
- The universe at some point in time began to exist.
- Therefore, the universe has a cause for its existence.
where x = "the universe" in steps two and three.
Mind, validity does only look at the structure of the argument and the logical relations between its elements. It is not concerned with whether these elements themselves do have some hidden relations. The argument does have the form "For all x, if x is A, then x is B; X is A; therefore x is B" (modus ponens), therefore, it is valid. Whether it is true is a question of soundness, not validity. And if you are to criticise the argument, you need to attack one or both premises and show why they are (or one of them is) wrong.
Also, this does not say anything about the actual nature of causation. It just states that there is a cause that caused the existence.
The last two steps now basically address the meaning of how we can understand "beginning of existence" and "cause". These two aspects of the argument cannot be discussed in isolation since causation and becoming are closely related. But this is where the first three steps are filled with life, as it were.
Premise one: Nothing comes into existence ex nihilo
Premise one is known since Parmenides and basically is an expression of the Latin phrase ex nihilo nihil fit: It says that given something is not eternal, this something did not pop into existence out of nothing (or: for no reason whatsoever). Its existence must have an origin, a reason, a cause. While not exactly easy to argue for as such, this seems to be how our thinking is hard-wired so most of us take this as granted.
Premise 2 and conclusion: Different forms of causation?
The conclusion and how premise two is to be understood cannot be looked at in isolation. Both only work together if we have a certain understanding of what "the universe" means and why everything, including the universe has to have a beginning.
You seem to assume that all causation (and thus beginning) has to be transformative, ie. has to transform stuff A into stuff B. After all, this is the kind of causation we build our very idea of causation on: natural laws governing the transformation from state A of matter/energy and spacetime to state B of matter/energy and spacetime. The Kalam argument actually argues that this cannot be how causation works for the universe. This has two aspects which only work in unison:
Form A: The conceptual argument regarding "the universe"
If "the universe" is taken to mean "all of material existence", then the beginning of the universe literally means that we come from a state A where there was no material existence (no matter/energy nor spacetime) at all to state B where material stuff began to exist in spacetime in the first place. Since Aristotle, people therefore assume that other than after the beginning of existence of the universe, the causation of the existence of the universe itself, if it has a beginning, has to work without material causation, ie. without the transformation of stuff into other stuff.
Craig does use a variant of this in point 4: Since there is no form of causation within the universe (laws of nature, the nature of matter/energy itself) which can explain how all this energy began to exist in the first place (no matter its form or distribution), we have to assume a form of causation from without, ie. a causation from something fundamentally different from matter/energy.
Form B: The infinite regress argument
The first three steps of the argument cannot be understood without the infinite regress argument. This argument basically says that there cannot be an infinite chain of (transformative) causation where the beginning of the universe is simply one step. There has to be a starting point for each causal chain. Actually, Craig does use this, as the SEP article points out:
In defense of premise 2, Craig develops both a priori and a posteriori arguments. His primary a priori argument is
1 An actual infinite cannot exist.
2 A beginningless temporal series of events is an actual infinite.
3 Therefore, a beginningless temporal series of events cannot exist.
You can read up the actual arguments (and counter-arguments) in the article, but the main point being is that no definite entity (and the universe is "definite" in the sense of a more or less stable, albeit changing, system with particular states of affairs) can be an actual infinite since infinites by definition contain everything of a certain class. In the case of the universe (all energy and matter in space-time), it would be every possible reality at every point in time, everywhere, which runs against what we experience.
Therefore, the infinite regress argument bolsters the premise that the universe (in the sense of all material existence) has to have a beginning.
If correct, this means nothing less than that, together with the conceptual argument, there has to be a creation/causation/beginning of the universe not out of matter/energy in spacetime (which would mean out of itself) because it cannot be thought otherwise.
A posteriori, he additionally uses the big bang theory as supporting premise two: If science says the universe came into existence out of a singularity some specific time ago and there was no spacetime nor energy distribution as we know it before that (and many physicists say so indeed), who are we to question that? This is, by the way, a problem with your assumptions: It is all but clear that stuff has always been there.
A short word on "causation"
I basically can hear you saying something along the lines "but wait, this is not how causation works!"
I think it is worth pointing out at this point that causation is just a conceptual relation between two states where the occurence of state A leads to the occurence of state B. Since Hume, we generally assume that this is basically only a habitual relation, something we observed so often that we take A to be the cause of B. As a shorthand, in a sense.
In the realm of laws of nature, this came to mean that there is a transformation of stuff into other stuff via a certain mechanism. That is a very peculiar sense of causation though which implies some "real" thing going on that exactly corresponds to this "causation" instead of what it really is: Two events between which we make a link. The physics "just happen" in a steady process, there is no isolated "causation" between two states. We just choose to take two distinct states more or less arbitrarily and inquire what happens in between, making the "causation" very detailed or, as in most cases, just a coarse approximation of what actually happens on a physical level.
It also does not mean that when we say "I willed this statue to come into existence, and so it came into existence" that the will to make the statue cannot be seen as a cause for its existence. Indeed, scientific explanations of causation break down as a viable explanation e.g. for the existence of pieces of art (at least for the time being). If you think about it, it becomes very handwavy very fast.
Thus, I would say that a concept of causation that only involves the transformation of states of energy in spacetime may be too narrow (for the time being).
Why natural vs. personal causation?
Now I will shortly address why there are natural/material and personal causation put up against each other as the only two possible kinds of causation in Steps 4 and 5. This has two reasons: historical and theological.
The historical reason is that basically since the writing of history, humankind does assume a duality of the material world and the spiritual/ideal/mental world and that they were following different laws. Therefore, it is natural to assume that if we need to assume a kind of causation different from material causation, this kind of causation would be one of agency: A will that works into the material world.
The theological reason is that not only since the victory march of the sciences, people feel that in a material world of nature, ruled by laws of nature, there is few to no space for God(s). Thus, if we are to make space for an acting God, it is natural to put this outside of the material world. And if that is true, and we need the universe to be caused, this person outside of the material world is the prime candidate to do so.
Weaknesses of the arguments
Generally, the whole part 7 of the SEP article discusses all weaknesses and points brought up for and against the argument, including variants for the formulation. I would like to stress and simplify two main weaknesses which are closely intertwined:
Metaphysics and epistemology
This argument makes assumptions about a state we simply cannot know anything about. Given there was a big bang with no matter/energy nor spacetime, for which there are indeed strong arguments to be made, we cannot infer anything about what there has been or how that was caused since all our ways of inference and our laws of causation break down until many milliseconds after the big bang.
A category error
I think your criticisms come down to one basic thought: These terms do not make any sense in this context. And there are good arguments in support of this intuition (apart from the "eternal stuff" part, as shown above). Basically, the argument uses different category errors, i.e. applies concepts to a domain where the concept loses its viability:
The concept of beginning relies on the existence of (space-)time. If there is no space-time, talking of a beginning does not make any sense. One of the logical problems is that the universe literally cannot have a beginning in the sense of point 0 from where its existence unfolds since there was no spacetime until after it came into existence. Beginning is normally taken to mean the point of time in which stuff was caused to exist, with the existence stretching from thereon. If there is no time before the existence of the universe, that makes it hard to apply the concept of beginning properly. It becomes an analogy.
The argument implies that personal agency was just a different kind of causation. This is problematic. Not only Kant, but modern definitions as well, say that causation has to follow laws. Thus, even if there was something like "causation out of freedom (personal agency)", it would have to follow laws and not be based on a whim of God thinking "It shall be" and thus it was. It is questionable whether the term "causing the universe" does make sense at all without some kind of law/mechanism which explains how there is a transition from state A to state B. And "some personal agent created the universe, we just can/do not know how" does, if we think about it, not explain the existence of the universe any better than "it just happened to begin to exist, we just do/can not know how" (creation ex nihilo). In a sense, it is creation ex nihilo through the back door.
Oftentimes in metaphysics, the existence of actual infinites is rejected as paradoxical/nonsensical. Actually, the historical arguments for a beginning of the universe strongly rely on this conceptual reasoning. The problem here is that constructs of the highest possible level of abstraction (mathematics, logics) are in a sense re-applied to the material realm directly, without any intermediate mappings - and this is bound to fail. The paradoxical thought only occurs in our application of concepts on how we think about physical reality. Just because it blows our minds if we try to imagine it as "real", it doesn't mean "we" and "our universe" are not only a local state in an infinite manifold.
I think the main itch you got is that we cannot possibly know or understand what it shall mean to be a cause of the existence of the universe. Even if we take it to be true that the universe is not eternal, thinking and laws just break down as soon as we reach point zero and the terms "existence", "beginning", and "causation" do not make any sense any more. As this is frightening to many, a lot of persons do not accept this as truth but search for consolation in an alternative that does not exactly bear any more explanatory power but fills the gaps with our everyday experience (personal agency) and longings, ie. a benelovent theological entity with the promise of eternal life.
Taken this way, the kalam argument only makes sense in the context of faith: If I believe in an entity that is eternal and can cause whatever it wants, then existence, causation, etc. can bear a specific sense in the argument which allows us to accept the premises. If not, the argument runs into several problems. But this is not because of the reasons you presented in your question.