It is my view that the confusion, here, lies in a mixing of different uses of the word "belief". We use it both to refer to faith, and to refer to current understandings and viewpoints.
Faith is taking something to be true in the absence of evidence. Viewpoints are more like hypotheses, and understandings come from evidence. As such, when someone is described as having a "belief in science", what they are usually saying is that they have the viewpoint that science is an effective method of obtaining information. They are not saying that, if science says something, it must be true - that is, they aren't saying they have faith in science. Note that there are exceptions - those who have true faith in science.
Those who have belief in science generally accept the conclusions arrive at via the scientific method. The use, here, of the word "accept" is important. Should evidence come forward that contradicts the accepted conclusions, then those who have belief in science generally accept the new conclusion in place of the old one.
Based on the problem of induction, nobody can assert with absolute
certainty that the laws of science (i.e. physics, chemistry, etc,...)
will hold all the time, in every part of the universe. Believing that
that is the case is therefore a form of faith, not knowledge.
Science doesn't assume that the laws of science hold all of the time, in every part of the universe. However, evidence has been collected suggesting that the laws seem to apply within the visible universe - motions of bodies seem to follow the laws of motion, light emissions from distant stars seem to have signatures that align with those of nearby stars (including the sun), which also match those of various chemicals on earth, after allowing for redshift, which is also consistent with our "local" laws.
However, should a celestial body be found with a signature inconsistent with what we have found, or should a body move in a manner inconsistent with our motion laws, or other such inconsistencies are found, science will update to account for this, and start investigating why this might be. The existing conclusion, that the laws we have found are "universal", will be replaced, either by determining new laws, or by accepting our local laws as only "local".
Current scientific consensus is that the universe doesn't stretch back
indefinitely into the past, but came into existence a finite time ago
with the big bang. The occurrence of the big bang and the subsequent
evolution of the universe are both driven by the laws of physics. The
laws of physics, seen this way, are the first cause of the universe
and the higher power that governs it's day to day functioning.
Again, this confuses conclusion with faith. The big bang theory was speculated based on various theories that apply today. From this theory, they then developed predictions about things that had not been observed (because nobody had yet looked), but that should exist if the theory is correct. For instance, residual background radiation from the bang itself. Observations then found what was expected, or at least close enough to support the theory.
And yet, science has a principle, coming from statistics, that nothing can truly be "proven" based on evidence. Instead, the evidence is simply of greater and greater weight as more of it builds up.
And even then, if science can't directly confirm something, there is always consideration of alternatives. We can't directly observe the big bang, and thus there are many different variations of it, all of which are consistent with observations. And even if we ignore those variations, the question of what came before the big bang is very much an open one.
Some, such as Stephen Hawking, think that the question of "before the big bang" is meaningless, that time itself began then. Others think that the universe oscillates (see "Oscillating Universe Theory"). And others believe that the time before the big bang had different physical laws. Some believe the universe is embedded in a greater universe, and that the big bang was merely the start of the substance of our universe, not the universe itself. Most, I would say, do not "believe" anything regarding it, considering it to be an unanswered, and likely unanswerable question.
Science does not seek to explain why the universe behaves the way that it does, only how. And for this reason, it can't really be considered a "belief system". It is rooted in the scientific method, which is a process.
Let me put it another way. If one were to create an analogy with religion, science wouldn't be the belief in god, it would be the meditation, or otherwise altered state, used to seek answers. Notice that meditation can be used by atheists just as easily as by anyone else - there is no inherent faith or belief tied to the meditation itself.
There are certainly some people who could be described as having "faith in science" - that is, rejecting anything that does not fit within science immediately, not as "unknown", but as "wrong". Richard Dawkins is a classic example of this. However, believing in science is not the same as this.
And even those with faith in science can't be said to be following a form of theism, because that would require a faith in the results, not in the process. Those with a faith in science would alter their view of the world if it were discovered tomorrow, by scientific techniques, that the apparent patterns of our world are merely happenstance, that even the imperfect laws of quantum mechanics were far more strict than the universe really is, that our apparent reality was nothing more than a massive coincidence of randomness. Their faith is in the method, not the conclusions, and believe that information obtained by other methods is necessarily untrustworthy (thus the disbelief in gods, which lie outside of the realm of science).