Norseman
Entirely Wholesome
It quite possibly wouldn't be a short time. Without the easy early conquests due to the Native Americans suffering apocalyptic plagues, the entire process is likely to take much longer if it happens at all. Both because the locals would be much harder targets, and the fact that without those early conquests the European powers will have a lot less incentive and resources to run a campaign of conquest in the first place. Both because it'll be harder and less rewarding, and because they won't get into such an extremely expansionist mindset to begin with without those early successes planting the idea that it was practical.
And the less incentive there is for outright conquest the more trade there will be instead, which means more opportunity for the Native Americans to buy or copy European technology and tactics further slowing any impetus towards conquest. In such a timeline instead of OTL empires built by genocidal conquest, the result would be more mercantile ones; like what happened to Asia. Not nice, but better than OTL.
Also, remember how much of OTL settlement was basically built on top of either graveyards or the aftermath of plagues. English settlements in North America? Benefitted enormously from moving into a former agricultural region where the previous owners had just died, leaving behind managed lands. Spanish conquests in America? Other than Mexico they also benefitted from things like the Incan civil war caused by plague.
Then we have the Mississippi and Amazon civilizations which were wiped out by plague. If they are still around then, well, that's going to have some kind of impact that's for sure. Especially the Amazon civilization, since that area was going to be hard for Europeans to settle no matter what.