An argument I’ve heard before is that God made the universe relatively recently (10k years ago or so) but with the appearance of age. Something like God “fast forwarded” through time to skip to the part where humans started recording history. In that theory both the majority of modern science and a strangely literal interpretation of the Bible can both be true at the same time. The scientists are unable to measure that God “fast-forwarded” the universe because he didn’t leave any evidence of it.

In my experience the majority of Christians don’t hold that view, but instead see Genesis as metaphorical, and thus it actually fits in rather well with the current Big Bang model. So well, in fact, that early on a lot of scientists rejected the Big Bang as “creationist rubbish.”