on the contrary: to the extent that they knew the word, native americans considered themselves americans, and the colonists did not consider themselves americans, but rather spanish, portuguese, english, or dutch, as the case may be
the idea that native americans were native to that continent (or pair of continents) was not in any way novel to them; what was novel was that there were other continents such as europe, and thus that there was a distinction between america and the world
so everything you have said is completely unrelated to the truth