The claim makes a ‘category error’, supposing that science and religion are trying to answer the same questions. This is not necessarily the case for all faith systems.
For example, I think it was Oxford mathematician John Lennox who said that he didn’t believe in a “God of the gaps” but a “God of the whole thing” - that he expects anything (within the limits of scientific explanation) can be explained by science and mathematics, but simultaneously believes the whole system was authored and is continually sustained by God.
For Christians and Jews at least, I wouldn’t expect that many people ever believed in God just because science couldn’t explain things (in comparison, I think a lot of polytheistic belief systems came out of trying to explain physical phenomena). It’s more the idea of revelation (through prophets etc.) and later the historical person of Jesus that would be the basis.
It stands to reason that a being that created order from chaos and gave form to the unformed would plausibly enjoy creating a universe that was internally consistent.
I don't understand why the universe needs to be mysterious or inconsistent to be created. I don't understand why it can't be (or at least seem to be) billion of years old for that matter.
That being said, I think God has to be a programmer - it’s the most efficient way to create something huge (the universe), while being predictable, and therefore knowing “everything”. The universe is just a huge - ok, really, really huge - state machine. And the programmer who wrote it can predict it’s state at any point of time.
This is the case now, precisely because any testable claim made by religion that conflicts with the evidence is eventually discarded. No amount of faith will let a demonstrably false claim stand indefinitely.