The term 'Native American' bugs me, because a) it implies that these folks sprung from the soil or something, and b) anyone born anywhere is presumably a native of that place so why are they considered the only natives? I'm a Native American (or native lowercase) American. So was/is a whole bunch of people, many of whom you may be familiar with.
Maybe 'aboriginal Americans' would be more precisely descriptive.
Or 'the people who got here first Americans.'
That I like the sound of.