Would it be possible to have a thriving human population after 4350 years if it started with only 7 humans such as noah's family?
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.
Two problems have been identified with starting with a starting population of seven. 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.
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.
Under a government which imprisons any unjustly, the true place for a just man is also in prison. Thoreau: Civil Disobedience (1846)
The apathy of the people is enough to make every statue leap from its pedestal and hasten the resurrection of the dead. William Lloyd Garrison.
“Choose silence of all virtues, for by it you hear other men's imperfections, and conceal your own.” George Bernard Shaw