If you were to distribute all people in the US uniformly, everybody would have about four soccer fields of space. If you distributed them over the forest area of the US everybody would have about one soccer field of space. In either case if you account for yards and access roads you wouldn't have what I'd call pristine woods anymore.
I feel like we should at least exclude people under 18. We can then, in addition, account for couples, and perhaps even prisoners/institutionalized, college kids, the military, and so on.
https://www.wolframalpha.com/input/?i=1+%2F+population+densi...