There have been times when much if not all of the globe has been under ice, so I suspect that, technically, there would be sufficient moisture in the world for such an event to occur.
Ice is around 12% larger, by volume, than an equivalent mass of water, so that's not necessarily the case. Similarly, whilst much of the low-lying lands in which humans tend to dwell, at high latitudes, was icebound, the majority of the tropical region never was, and the higher areas similarly weren't.
We don't know what the population of the world was at the time, but in view of the fact that the global population was less than one billion until the early 19th century, they couldn't have been 'bonking' all that hard.
The problem isn't one of geometric progression, it's more to do with the degree of genetic diversity that's apparent in humanity - and other species - which isn't consistent with having such a small population of humans as the common ancestry of all humanity barely a few thousand years ago.
Since the passage about the Flood occurs in a section of the Bible that is theological rather than historical, Bible literalists don't really have much to explain.
Well, they do, because there are literalists out there who don't think that any of it's solely theological, they genuinely believe this actually happened, within the last six thousand or so years - I appreciate that you aren't one of those people, but they are out there, and in alarmingly large numbers.
Its odd that you clearly think that this passage was meant to be historical!! 
Not really, given that some people who accept the validity of the work make that claim. I don't doubt that it isn't true, I've no idea if the authors originally believed it was, believed it was a reworking of an older true story rejigged for their time or if they knew it was nonsense in their own time but thought it added something to the book they were writing.
O.
