If they don't die in a droves, supposedly due to transported disease from the Old World, they will make their bones as a majority-indigenous continent akin to the former, and at worst, end up more like the western-imperialized people of Asia and Africa that later fights back rather than the near-genocided state they are known as, today...
That's why I'd do it about 1000 years before, to give the American population time to bounce back.
If despite the previous disease exposure and skills given, they die in similar amounts during the European conquest, we can more certainly conclude it was European imperialists and settlers, such as by their scorched earth tactics, and forced labor plantations, whose policies more purposely seeked to eliminate them in the early 1500s-1600s
I figure if they have iron or steel weapons, along with cavalry and other various animals to serve as beasts of burden and food sources, they'd be able to defend themselves from the Europeans pretty adequately no matter what.
Lennox