Hi Picnic;
A very simplistic way of looking at things:
Science says the Earth is old.
A literal reading of the first few chapters of Genesis would suggest a young earth.
Therefore either science is wrong or reading the first few chapters of Genesis literally is wrong. How do we decide which is wrong and how much should we let things external to the Bible influence our interpretation of the Bible?
As was observed, a very good question. When two things we believe are true are in conflict, that presents us with a paradox. So lets back up, should be believe the current thinking of science is true? Or has scientific thinking evolved over the years, changing what was thought to be true in the past to falsehood as the new view replaces it? Yes. Therefore we should not view current science as necessarily true, but just what seems true based on the state of our knowledge at this time.
And we can view the Bible in a similar way. We can accept the Bible as trustworthy and reliable while also accepting our understanding of the Bible may be flawed around the edges. It was written by men, primarily for the audience at the time, and so, as was also observed before, it reflects the world view of the times. When we say, to the ends of the earth, we do not now think of a literal edge, but rather to the ends means as far as we can, which is everywhere. So the principle, everywhere we can, remains trustworthy, while the world view that the earth has literal ends and corners is flawed.
Lets turn to Genesis 1 and 2. If we "interpret" the meaning of "day" to mean a twenty four hour day, then the Bible does suggest a young earth. But if we "interpret a "day" to be an indeterminate period, the the earth could be way more than 6000 years old.
So we have at least three things in play. One, does the Bible contain the mistaken views of men? Two, is our interpretation of the Bible flawed. And three, is the current view of science flawed. Based on this, I think any jury in the land would have reasonable doubt about whether the Bible is actually untrustworthy.
Final point, please read Job 38. It says we do not know how God created the heavens and the earth because we were not there. That leaves us with "God did it either supernaturally or naturally or in some combination of both." I think Paul would say, that is a trustworthy statement. God Bless