Every argument about God is a philosophical argument about existence, consciousness and causality
The existence/non-existence of God falls within the field of metaphysics and hinges on one's views on existence, consciousness and causality. The position is heavily informed by epistemological principles relating to the onus of proof, and the admissibility and evidence required for assertions of causality and consciousness.
Most arguments relating to the existence of God come down to deciding which of existence, consciousness or causality has primacy in metaphysics --- i.e., does an existing thing always need to have been caused by some other thing. Scientific theories like the Big Bang really do not change the philopsophical argument at issue. Assuming you accept the Big Bang theory it just pushes the argument one step back --- i.e., what, if anything, caused the Big Bang?
The argument you give in your question does not really address the fundamental philosophical question at issue, and it has a lot of glaring problems that would be simple for a sophisticated theist to dispatch. Indeed, I would go so far as to say that the premises here pretty much guarantee that a sophisticated theist will back you into a corner where you have to concede the essentials of their position. Below I will point out some aspects of each of the elements of your argument that are weaknesses for an atheistic theory. At a broader level, it is wrong to think that you can substitute science for philosophy --- no scientific theory is ever going to oust philosophy on this issue.
(I actually don't think what you have given is a serious scientific argument against theism at all. An atheistic theory requires acceptance that there is some primary in existence that was not itself caused by a previous thing/process --- i.e., that it just exists. Consequently, any serious argument against theism is going to adopt an epistemological view that precludes arbitrary assertions of causlity, and it is going to interpret causality as applying to the actions of existents, rather than to ther existence. This will be a philosophical theory that is logically prior to science in the hierarchy of thought.)
The Big Bang implies that the creation of the Universe occurred as a direct result of scientific processes.
This first premise asserts that the universe "occurred as a direct result of scientific processes". This is an asssertion that the universe was caused by an underlying process, so it then behooves you to describe the process that caused the universe. Either you can't do this, which opens the door for a theistic explanation, or you can do this, and you just push the question one step back for the theist (i.e., what caused the things/processes that you say caused the universe?). Alternatively, if you try to appeal to an alleged cause that is itself outside of the universe, you are then coming onto the theists turf and conceding a substantial part of their position.
Scientific processes are well-supported and clearly evident in shaping the physical conditions of the universe today and the beginnings of life.
The theist can easily concede this point without damaging the ultimate question of what, if anything, caused existence. Indeed, most sophisticated theists will probably claim that the reasoning underlying science supports their own theistic position (i.e., looking for an underlying cause for things/processes), so they will be quite happy to agree on this point and then use it to beat you over the head later.
Science is capable of explaining all undertakings and occurrences in the universe.
Assuming you want to follow science (and it seems clear you do), this premise commits you either to an infinite regress of causal explanations of the existents in the universe, or else a causal assertion that the universe is caused by something outside the universe (which is exactly what the theistic theory provides). By implication from this premise, if your theory of existence ever runs out of explanations (e.g., if you ever get to a primary existent whose occurrence can't be explained from some previous existent that is also in the universe) then your theory is non-scientific. You have posited that the Big Bang caused the universe, so now explain the occurrence of the Big Bang, then explain the occurrence of the thing that caused the Big Bang, then the occurrence of the thing that caused the thing that caused the Big Bang, and so on ad infinitum.
If you adopt this view of science, now you are screwed --- the theist will simply push you further and further back and commit you to an infinite regress of causal explanations. When you inevitably run out, the theist will give you a theistic causal explanation for your primary, using God as an entity outside of the universe which caused that primary. At that point, according to your premise of what science is, your theory is non-scientific (because it can't explain an occurrence in the universe) and their theory is still potentially scientific (since it can explain this without adding any new thing in the universe that itself requires explanation).
As you can see, this premise will deem any atheistic theory of existence non-scientific, since any atheistic theory of existence is going to have to choose a primary which does not require any further causal explanation, and your premise here deems any such theory non-scientific. So, far from seeing this as an element of a persuasive atheistic theory, this seems to me like a sure-fire way to kill your atheistic theory and provide the theist with the mantle that they represent "science" while atheism is "anti-science".
Therefore, the Big Bang, and subsequently the creation and formation of the universe resulted entirely from scientific processes, making the existence of God as an omnipresent and omnipotent creator of the universe impossible.
It's unclear how the second part follows from the first. As to the first part: Cool, so what caused the Big Bang?
Hmmm, since science requires every occurrence to have a causal explanation (according to your premises), perhaps an entity outside the universe caused it? An entity outside the universe that is so "potent" that it caused the entire existence of the universe ---i.e., so potent that we might reasonably call it "omni" "potent" perhaps. What, pray, might we call such an "omni" "potent" entity outside the universe that caused the Big Bang (or the thing that caused the Big Bang, etc.)?