And it's quite possible the Indians replaced and destroyed people who were already there. Who may have been more closely related to Australian aboriginals. There seem to have been some studies of some very old remains found in South America, and the people who lived in the southernmost tip of South America when Europeans first started to explore the continents, and of whom there were still few people left when DNA testing finally came possible, seem to have had some markers, if I remember correctly some articles I read maybe about 10 years ago.

But yes, immigration has been going on about as long as there have been people, but most times, when it happens in the very large scale, it means that the previous culture, and possibly most of its people, will be destroyed, one way or another.