Science seems to admit that it can't investigate ghosts, miracles or an extra-dimensional God. So, there is apparently a big problem of epistemology to start with.
This is because all these represent causal agents whose actions do not necessarily repeat. Therefore it's impossible to put together a hypothetical chain of predictable events leading you back to the starting point.
But, said otherwise, science can be to critique itself. In that sence, maybe it doesn't prove how things were, but it does prove the limits of science to prove anything. Again, we are back to your question of epistemology.
Well, you can come to dead-ends in science, like the BB, or QM phenomenon, or the inability to explain design, but you can also come up with scientifically valid natural explanations that are still not true. This is my main concern, because conventional thinking among many christians is, if you can explain something scientifically, then we should favor that over the supernatural.
Here's an illustration showing the problem with that. If a post event observer saw the jugs of wine after the Cana wedding, he could examine the evidence and put together a perfectly valid natural explanation for how the wine came to be (which would include time and natural processes). And since his explanation is scientifically valid, he would then be inclined to favor that over the testimonial evidence that this was a miracle of Jesus, which only happened a short time ago. His explanation would be scientifically valid, but historically untrue.
I think creation science is better at providing critique than solid conclusions about how things were. In some respects, that depends on your expectations. If you scale back your expectations, creation science works just fine.
I actually think creationist arguments are very good. The problem is, if you tout them as "scientific," you are puffing up this particular epistemological method which we all agree has limits. From there, millions of scientists start shaking their fists (somewhat justifiably) and sincere christians and theologians get swayed. They likely reason, "If science is the ultimate, end all epistemology, then maybe we're not reading the Bible correctly."
One knock from TEs is that creation science is not valid until it provides viable models for things like origins. Given the epistemological problem, there is more chest beating there than solid logic.
But are they even aware of the problem? Are creationists pointing out the fact that supernatural causation will confuse and almost always distort scientific interpretations? Creation arguments, I think, are
logically sound, but do they undermining those arguments by calling them
scientifically, sound?? In many minds,
scientific means
naturalistic.
In the way that the OP states the dilemma of working with the evidence, isn't it interesting that we get back to the question of whether man can indeed become like God in taking upon himself the task of discerning good from evil. You take the same evidence and all you get is a fight about whether the conclusions arising from that evidence are good or evil.
There's no doubt that people will always interpret evidence differently by their own choosing. But the tendency of christians to lean toward scientific naturalism seems much broader than it should be. I suspicion that many good creationist arguments aren't registering with the masses due to an equivocation of terms. Our side has one definition of
science, there side has another. This will often lead to what logicians call the four-term-fallacies.
Creationists are establishing the premise,
Science (our particular meaning) will lead us to truth
So the masses reason,
Millions of years is the conclusion of science (their particular meaning)
Therefore millions of years is truth
Looks perfectly valid, but there are actually four terms in that syllogism. It must be limited to three to be logically valid.
But then from there,
Millions of years is true (or right)
An exegetical approach to Genesis does not allow for millions of years
Therefore, an exegetical approach to Genesis is not true (or not right)
This syllogism actually is valid. The premise is false and therefore the conclusion is false, but the argument is valid.