The Great Flood? Never happened. Because if it had, the Australian, South American, and North American continents should have been devoid of animal life and people. But they weren't.
You have to bear in mind with "born again" Christians and other Bible believers that their starting premise is God exits. In fact for purposes of the Bible God having existed will do the trick.
For Joshua to stop the Sun in the sky the earth had to stop spinning so everyone should have flown off at between 700 mph and a 1000 mph or so. HOWEVER, if God existed He could change the laws of nature, suspend them, have them work a different way in different places etc. If God wanted a talking snake in the Garden of Eden he could have had a talking snake.
Think of it this way. I think it is fair to say fitting a 27 litre V12 Rolls Royce Merlin engine in a Toyota Corolla is impossible. However, for Toyota things are different since they make the Corolla and could bring out a new Corolla with a 27 litre V12 engine. In other words they are not stuck at the impossible as they don't have to convert an existing Toyota Corolla.
Personally I can't see any difference between the "born again" and the atheist. Neither have proof but their belief is strong to become faith. Faith is an extension of belief in the sense that without proof faith means you will act on something or have a very definite position.
As a small example. Tomorrow a mate of mine is coming here at lunch time. Of course I don't have proof he will be here. However, I not only believe he will be here but I have faith because I have acted on him coming here tomorrow, related to some other arrangements. However, if it was one of couple of other mates I would say to the other people "a mate of mine is supposed to be coming here tomorrow and I believe he will but I will call you about 11.30am as by then I will know for sure"