So called Native Americans simply emigrated to North America earlier, that's all.    No land bridge ever existed between Europe and North America, like the Bering Land Bridge that existed between Asia and North America during the last ice age.   While Greenland was connected to North America back then, the ocean between Greenland and Europe was just too wide and deep.  

If such a land bridge had existed, prehistoric Europeans would have been able to walk here earlier too, just like they did.

Native Americans are simply early immigrants from Asia.