I just want to be clear: you’re saying that “The universe is a lot older than six thousand years” has zero degree of confirmation, that we’ve not confirmed at all that the universe is billions rather than only thousands of years old. And you’re saying also that the universe’s being billions of years old is no more probable than the universe’s being only several thousand years old. Is that what you’re saying?
If so, you’re confusing science with theories about science. It’s possible to succeed at doing something without understanding how it’s being done. As I said, if philosophy of science hasn’t yet figured out exactly how inductive reasoning works, so much the worse for that philosophy, because science evidently has established that certain scenarios are much more probable than others.
Hume showed there are always other logical possibilities besides those entertained by an empirical generalization. But scientists aren’t doing armchair reasoning; they’re detecting real patterns in the natural order, and they’re doing that in part by narrowing down the pattern by falsifying the alternatives and by corroborating hunches by confirming predictions made by the hypothesis.
Logically speaking, those patterns could change at any moment as a “result” of a miracle. Whereas I’d never before flown just by waving my arms, maybe one day I’ll be able to do so. Such changes would be logically possible but naturally improbable. If we assume miracles can happen, science comes to an end. As I said, science and methodological naturalism have at a minimum a pragmatic justification.