What do you assume about the population growth rate of the first population to come over into the Americas?
Stupidity is assuming the present growth rate is constant and consistent, that it is a ceiling beyond which a population cannot exceed in populating a new continent - and a floor below which a population with diminishing resources cannot fall.
That certain populations or nations had set backs is reasonable, but the world population continues to grow. It grew even during the World Wars - because the rest of the world was multiplying more than the number who died in the Gulags and concentration camps and battles. Same with plagues, etc. At any rate, it is not a “proof,” but simply indicates that a relatively young human race is plausible, even probable, whereas posing a human race in the hundreds of thousands of years old does not match up with even a miniscule growth rate.