Putting on fast forward is fine. A rapidly expanding population, though, leaves very clear genetic traces. Whatever genetic variation was in the original tiny population remains, at a frequency not too different from what it started with. For Noah and family, that would mean a minimum frequency of 10%, since there were 10 independent copies of the genome on the Ark. As the population expands, some of those variants will drift down in frequency some, so that you'll find lots of variants in around 10% of chromosomes (and around 20%, etc), some around 5%, and fewer and fewer as you look at rarer variants. There will also be a sprinkling of rare variants, from new mutations.
Real genetic variation data looks nothing at all like this. There are roughly ten times as many variants at 1% frequency as there are at 10%, and more than a hundred times as many at 0.1% frequency.
So that's the challenge: explain why there are millions of low frequency genetic variants in the human population.
ETA: Mind you, that's not the only genetic problem with the Flood, but it's probably the easiest to explain.