[SauronOfMordor]

They would not only have had to be very nomadic but able to adapt to the multitude of changing climates (each containing a different mix of new plant and animal life) as they travelled from North to South America. That is a pretty tall order.

As Physicist pointed out, that's only 10 miles/year. We don't know what kind of poulation pressure would have impelled them to keep moving as new people crossed over behind them. If we assume a coastal fishing people, they could move their villages large distances without trouble and not caring that much about minor changes in climate

[Question_Assumptions]

When you move North to South, the climate changes are not minor. Jared Diamond wrote a book explaining some of the implications of West-to-East migration vs. North-to-South migration on cultures and civilizations. I'm sure that these problems are coastal, as well (e.g., if you hunt seals and use the skins to make boats, what do you do when the species you hunt stops?).