I also don't think there is neccesarilly a connection between abundance of food and population size when it comes to societies like they had

Unfortunately the archaeology disagrees with that. You also seem to be making these really broad statements encompassing a variety of cultures over 30,000 years.

The fact is Native American populations exploded and grew in "complexity" with the arrival of domesticated crops such as corn, beans, and squash. That's when we saw permanent settlements develop across various cultures. Simply put they were able to feed more people and move less because they had more food. You see this pattern repeat over and over as these crops spread across cultures.

I have heard that in some parts their diet was over 90% meat

There's a lot to breakdown here. Let's start with "their" diet. Diets varied wildly culture to culture, region to region, and across time. The diets of the Mississippian culture of the Southeast looked radically different than the diets of the contemporary peoples of the Pacific Northwest. Even looking at contemporary groups in the southeast you see that people on the coast got most of their calories from marine sources, but you go inland and you see a huge increase in the reliance of corn.

The only groups I can think of hitting that 90% number would be the various cultures of the Plains, the Innuit, and mostly every group during the Paleo period (it was the ice age after all pre-domestic crops).