Quite what you would accept as a proof of falsehood I don't know. There is no geological evidence whatsoever of a global flood about 4000 years ago; nothing of what we would expect to see if that story is true can be found. Likewise there is no genetic bottleneck, on the contrary the genetic diversity of humanity and other species whose genomes have been mapped is far too great for humanity to originate from 8 people that recently. (The situation for other species, with their 2 founders from the ark is even worse). You can argue that God "fiddled" to create the current appearance of no flood and excessive genetic diversity, but the possibility of such fiddling makes any disproof of Biblical writ impossible, since any contradictory evidence can then be put down to God editing the evidence for inscrutable reasons of His own.
I argue no such thing. Again, I go back to intrepration of the data and our understanding of how things "should" work. I genuinely believe that we don't even know what we don't know about genetics and dating.