Well, let's think about it.
It's 1600 miles at the closest point between South America and Africa.
In the last Ice Age, that was about a sixth smaller due to more exposed continental shelf, so it was about 1250 miles apart.
Continental drift is only 1.5 centimeters per year, so even if humans originated in sub-Saharan Africa 100,000 years ago, the continents were less than a mile closer due to drift.
Assuming that the ocean currents were about the same, the North Equatorial Current goes East to West at a speed of about .5 miles per hour mid-ocean, accelerating to 6 miles per hour when close to the Brazilian shore. We can assume an average of 1 mile per hour across the whole length.
The trade winds blow west to east down there, at substantial rates of speed, but paleolithic man didn't have sails, and without sails even a 20 mile per hour wind won't blow a log at 20 miles per hour. In the days of the great ragwagons of old, a warship under full sail in the Horse Latitudes MIGHT get 4 knots with every inch of sail tied on.
If we are GENEROUS, a stiff breeze could have added a mile per hour of speed to a hollowed-out log making the crossing.
So, there's 2 miles per hour of natural way on, to get across 1250 miles of Ice Age ocean (it was still warm in the tropics, and food is possible to get sometimes, when you're that close to a warm ocean teeming with fish...assuming you know how to fish...).
Without paddling, that's a 650 hour crossing...about 26 days...less than a month...WITHOUT paddling.
But suppose you paddle?
Add 1 mile per hour for paddling, and assume that the boats are paddled half the time. That's a 500 hour passage...21 days...3 weeks.
It's possible.
I don't believe that stone age man could cross the GIUK Gap, although I haven't really looked at how close IT all was under the ice. I don't think stone age man could survive walking months and months on the ice pack, like Elves crossing the Helcaraxe. Though it's possible. Eskimos do it.
I do find something more than vaguely suspicious about the efforts to, for example, show that the Celts were the first settlers of New Zealand et al, don't have anything to do with really looking at what happened, and have a lot to do with racial and political beliefs.
If America was populated from the Old World not just by Asia, geographic proximity, currents, weather and warmth makes it probable that it was done by Africans from sub-Saharan Africa, and the unique coloration of American Indians is due to the mixture of the Asian and Black races.