It seems that the more recent views by the archaeologists of the timing of the crossing from Siberia into America give or take 13,000 years ago was done the way you describe, that is, in small boats hunting along the coastline. Previously, the majority held that the early hunters came through a valley in Alaska which had warmed enough to form a corridor through the ice. Recent archaeological discoveries and carbon dating has shown that the people actually came before the corridor was opened, that leaves the boats.
Has to be by boat. We know when people first crossed into Australia ~ and it had to be by sea since the ocean never get low enough to allow some other form of crossing.
Wooden boats just don't last!