They walked across on the ice during the last Ice Age.
These people have European DNA:
Bye, Bye Beringia (8,000 Year Old Site In Florida)
"At Windover, more ancient human remains were discovered than the total of all others found previously in the New World, and they were the oldest."
Years ago, I read an article postulating travel by boat along the southern edge of the northern ice cap, from Europe to North America. It suggested that hunters of seals and other marine prey could have been caught in a storm and, trapped by the ocean currents, left no choice but to continue westward, thus discovering America. However, after the bad weather had ended, by following eastward along the ice and porting across the ice when necessary, two-way travel could be possible.
I believe that man noticed that things floated not too long after there was such a thing as a man, and that boat technologies were developed not too long afterward. The self-evident (to me) advantages, while terrifying to a landsman, wouldn't terrify everyone.
Thanks for the links; I'll check them out.