Thor Heyerdahl thought it would only have taken about ten years for wandering tribes to have traversed North America. (There was no reason for anyone to remain in the bleak, snow-covered north, when bountiful lands with plenty of game
were just head of them.)
Why would you move camps so often with abundant and stupid big game everywhere?
I would think a 20 mile per year pace to be more likely. That would be about 1-2 hundred years to cover the two continents.
Starting from a very small base of maybe 70 people, and doubling every 20 years, roughly, it takes a hundred years to reach a couple of thousand people. You are up to 70-140 thousand in two hundred years, and close to 40 million by the end of the third century of colonization.
Genetic studies show the base to be very small, indeed. The over-all pattern that is emerging suggests that the Americas were colonized by a small number of individuals (effective size of about 70), which grew by many orders of magnitude over 800 – 1000 years.[21][22] The data also shows that there have been genetic exchanges between Asia, the Arctic, and Greenland since the initial peopling of the Americas.[22][23]