Off the top of my head I think it's supposed to be 1600 yrs after Adam, so about 4400 yrs ago not 3400 yrs ago.
As to having a go at answering your question, ...Umm there's a hell of a LOT of water on this planet. That could easily be argued to satisfy your question, or not depending on your angle... In fact any satisfactory answer to your question can be argued away as well, because it is too easy to do so and it depends on what your are looking for in the way of an answer. Pro Noahs Ark or Pro Evolution.
For me, the more I look into Noahs flood the worse it gets. However......
I did do some basic (note basic!) research into population growth thru the ages and that did throw up some interesting points. (This again is all off the top of my head)
E.g If the population were to double in size every 150 yrs then it could easily achieve many billions within 6000 yrs. If it were to double every 80 yrs then it could easily achieve the many billions we have now after just 4400 yrs since the "flood" (yes allowing for death rates). Statistically population tends to double faster than that at about every 40 - 50 yrs currently although that is flexible and by no means fixed. So in other words it is easily possible to go from 8 people 4400 years ago to 7 Billion living now. Which then raises the other side of that point... If man is 100,000s of years old and there havn't been any Mass Extinction Events in the recent 100,000 yrs then why are there so FEW people on the earth? This DOES raise an interesting line of reasoning. But it looks flimsy when you consider the animal questions though.
After that the problems go deeper than that though, because throwing out Noahs ark throws out Christ, The Bible and quite likely God as well. Christ taught using Noah as an example, if it was just allegory then he was lying by doing so and as such greatly undermined his credentials.
Cheers