Science can’t disprove religion. In fact, science can’t disprove any supernatural idea. It’s at this point that many theists would be happy to celebrate and claim victory over empiricism but simply because science has nothing to say about the matter doesn’t mean that no rational inquiry need apply.
For instance, science can demonstrate that the world doesn’t appear to be 6000 years old but it can’t disprove what is sometimes called the Omphalos hypothesis, the idea that the Universe was created by God with features that made it appear older than it was. So, the creationist would say, the Earth seems to be billions of years old and species seem to have evolved largely through natural selection but God only made it look like that way. Appealing to God like this isn’t predictive, unless you are to argue because you know the mind of God that it had to create a universe that appears as ours does, so whatever universe we do observe is just one of an infinite possible number of theistic universes because God could theoretically make the universe appear any age. This means the appeal to God has not narrowed our expectations of the apparent age of the universe but merely appealed to one of an infinite number of scenarios. Contrarily the age of stars, the cosmic microwave background radiation, Hubble’s law, etc. all independently serve to predict the age of our universe to be within a limited range and the fact they all converge on a similar age greatly reduces the array of possible answers for the actual age.
If, as a friend of mine likes to say, you know you have a rolled a three on a die and you posses only a four-sided die and a twenty-sided die which die is it more likely to that you rolled? Obviously it is the four sided die and it would only become more likely if you instead possessed only a four-sided die and a hundred-sided die. Expanding the larger die out to be infinite-sided, as supernatural explanations do, doesn’t mean that you can no longer reason about which is more probable. Quite the contrary, it becomes vastly more likely that the result is from the die with less possible outcomes.
What this analogy highlights is any supernatural solution to disconfirming evidence which places that theory firmly outside of the field of science just appeals to a “explanation” which is not predictive and infinite in scope which must be weighed against more limited range of natural predictive explanations which would explain the phenomena. This same principle holds for claims that psi-phenomena do exist or that prayer does work but only when they aren’t tested, that species only seemed to have evolved and existed based upon survival and so on for every attempt to explain away why our observations don’t match up with a supernatural phenomena. So just because you can never demonstrate using science that the entire universe wasn’t created last Thursday that certainly doesn’t mean it’s probable or reasonable to conclude that it was.