My understanding is that the linguistic evidence also supports 3 waves. With the Inuit being the most recent. The first wave languages occupied all of South America, central America, and much of North America before European Languages replaced them.
This is a good discussion of ancient origins of the original american inhabitants. My great, great grandmother was 1/2 ojibwa(canadian tribe)back in the civil war days. As silly as it sounds, back in the jimmy carter days and minority hiring on construction projects, my dad went back to MN and got himself declared an ojibwa tribal member(for “consideration” of course). Thus as a electrical contractor he was the usual 10% minority on construction projects. Silly, but true....