I don't understand the point of your question. If there was no global flood, then there is scant reason to wonder how the earth got repopulated in only 4300 years.
I am confronting just portions of all the objections to the biblical account of the flood. I realize there are serious problems with the idea of a global flood. But for the sake of argument, I want to know the possibilities of repopulating the world with just noah's family because the objections to the other problems could be resolved in the future with knowledge we do not now have.
Two problems have been identified with starting with a starting population of seven.
I realize the diversity of the gene pool is not possible coming from 7 people 4350 years with current biological knowledge. We cannot solve all problems at one time. I have already addressed the problems of inbreeding.
A third problem is that reducing all of earth's population to 7 only 4300 years ago makes it extremely difficult for all other historical events to have happened during periods contemporary with the post flood period.
What if we have misinterpreted the bible and the flood was earlier than 4300 years ago like 7,000 years ago? Would that still make it extremely difficult for all other historical events to have happened in the post flood period?
The fourth problem for some people at least is that it renders the flood story in Genesis as a rather allegorical, if not fanciful account.
No need for this problem if you realize that our understanding of a supernaturally inspired text written to a people and time far removed from us is not always going to be accurate. Resorting to naming a text as allegorical when a straightforward reading gives problems scientifically, is not the way to go IMO. There are a myriad of literal interpretations of biblical texts. The modern mind ,however, only grasps one particular literal interpretation when the ancient mind had a completely different idea when it was written.