The point is whether or not it is possible to grow a human population of significant size from just 7 people in a short amount of time.
Most biologists reckon you need a minimum viable population (MVP) of thousands for larger animals to survive.
An MVP of 500 to 1,000 has often been given as an average for terrestrial vertebrates when inbreeding or genetic variability is ignored. When inbreeding effects are included, estimates of MVP for many species are in the 1,000s. Based on a meta-analysis of reported values in the literature for many species, Traill et al. reported a median MVP of 4,169 individuals
So, it is possible. How do we know how fast global human populations grew in the past? From the biblical records, the families of each generation appear to be quite large. It doesn't take too many of that kind of generational enlargement to get an enormous population rather quickly.
Your biggest problem is working out how Noah's family survived the first few months.
There would be no food - they can't eat animals and there's no grain. The land would be hundreds of feet deep in mud - everywhere; farming would be impossible. Disease would be endemic as everything that was once alive is now rotting.
Life, don't talk to me about life - Marvin the Paranoid Android