It is speculated that Asians came to America along the edge of the icecap. The same speculation can be made of similar travel across the North Atlantic., which is a shorter distance. Why not?
There is some very old stuff, ruins and pieces of handtools and things like that, that obviously came from the direction of Europe and Africa. They could hop over starting from the Canary Islands or Cape Verde to the West Indies in their bigger wood boats no problem. Crossing on the Pacific side would involve going three times farther before they arrived someplace. There shouldn't be any question about this.
If you go from Europe to North America along the North Atlantic litoral, you have one of the world's highest flow rivers feeding icebergs into the North Atlantic. It's called the St. Lawrence.
The Pacific trip is easier than the Atlantic trip.
On the other hand, should you attempt to return (using paleolithic technology), you will simply not make it ~ these are both one-way trips!