Native Americans crossed the Bering Strait and would have had to pass through North America. So how did South America end up with a more dense population?
The simplest answer is that agriculture was invented in Central and Meso-America and the Andes and Amazon regions of South America. But no staple crops native to North America were ever fully domesticated, and instead agriculture diffused from Central and Meso-America up into North America slowly over many 1000s of years, giving Central and Meso-America a head-start over North America in rapid population growth.
Maize corn, beans, and squashes were native to Central and Meso-America. Potatoes and quinoa were native to the Andes region of South America. Cassava was native to the Amazonian region.
The domestication of staples crops such as maize corn and squash began around 10,000 year ago in Central and Meso-America. And agriculture supported rapid population growth in these regions.
But it took several 1000s of years for varieties of these crops to eventually arrive in North America on account of the fact that the climate in North America was very different from the climate in Central and Meso-America.
Firstly, there is large area of desert in what is now northern Mexico and the southern US. The earliest domesticated varieties of maize corn, squash, and beans were most well-suited to grow in their native tropical and subtropical climates of Central and Meso-America. Varieties of these staple crops had to be bred to thrive in more arid desert climates before they could be extensively disseminated through these regions of North America.
And secondly, the rest of eastern North America has a much colder and more erratic temperate climate, and yet more new varieties of maize corn, squash, and beans had to be bred to thrive in these erratic temperate climates before they could be disseminated even further north.
Maize corn, squash and beans could not be effectively farmed in alpine climates. So they never made it across the Rocky Mountain or Sierra Nevada Mountain ranges, which basically meant that the people’s of the Pacific Coast of North America from California to Canada never received agriculture until after the era of European colonization.
The longer it took domesticated staples crops to reach a new climate zone, the slower the population growth was in those regions.