Pretty old. Billion of years perhaps?
The YEC flood model has the flood taking up and laying down huge layers of sediment, creating fossils, causing massive uplift and destruction. Science attacks this model therefore making it it's 'flood model' as well. The biblical model does no such thing.
Both YEC and science envision a highly destructive flood going far beyond what God intended the flood to do. A good example would be the ark. Science says that such a structure would be destroyed by the flood as they envision both the ark and the flood. And of course it would be. But the story has the ark successfully resting on a mountain after the flood recedes, therefore all flood conditions and the integrity of the ark were substantially different than is commonly supposed. One cannot attack just one aspect of the story i.e. "Well, the ark would have sunk, therefore the whole event never happened."
Note that the ark was 'lifted up', not washed away in a tsunami-like flood. This suggests slowly rising water, which is supported by the time frame given in the story. If slowly rising, and equally slowly falling, whence all the destruction?
This would explain the 'missing' evidence. There is no 'evidence' of a massive, tsunami-like, gully washing, mountain moving, sediment making flood, because that flood didn't happen.