Now, it's only my suspicion, but I kinda suspect that folks drifted around. From a North polar perspective there are quite a few islands (many inhabited) between NA and Europe -- it wouldn't have been difficult to journey from one to the other even before the Vikings.

Journeying down a coastline in a boat is easier than walking....

Mitochondrial DNA analysis might help here, as would underwater examination of now-flooded potential coastal campsites (which is being done).