I was born in America. Therefore I consider myself a Native American. The USA is the only sovereign nation to which I owe any allegiance. It is the only nation where I have had citizenship. I don't have divided loyalties as some of my fellow Native Americans unfortunately have.
I choose to stay out of your debate but would like to make one correction. Unless your family is indigenous to the Americas (North or South) you are in fact a descendant of immigrants, most like Europeans who came to the Americas after the 15th Century.
The most current belief is that the first humans came to North America via a land bridge from Asia to Alaska 25,000 years ago. And these people fought with each other and conquered each other many times over before 1492. Thus, there are no people in North America today who can claim they are from indigenous stock.
I've read & heard that very story since I was a kid being that my Maternal Grandmother is Native American, no argument in that fact, 25,000 years which can be debated give or take a few thousand adverse to 500 years which is well documented throughout history. The premise here, the native American has more of a justified claim of squatter's rights if that term may be used. So as you've stated, no indigenous people exist technically, maybe with the exception of those created in the Garden of Eden.