I sort of see this the other way. There’s absolutely nothing in the scientific record that can disprove the possibility that the world is 4,000 years old. The scientific method makes certain claims about the state of the universe 4,000 years ago. Now assume that God created the universe—fossils and all—to look exactly like that 4,000 years ago. That’s obviously a religious hypothesis rather than a scientific one, but it’s consistent with the evidence and doesn’t anyone to believe in a scientists’ conspiracy or anything. Of course this would mean that God is perpetrating a massive conspiracy, which would be an odd thing for a just and moral God to do. But people believe God’s up to all kinds of odd stuff.