Even since the inundation of Beringia, the distance over water you would need to cover to get to the Americas starting in Northeast Asia and arriving in Alaska seems drastically shorter than trying to cross the Atlantic from Europe or North Africa. And yet, the West to East route was discovered twice that we know of (the Norse, and later Columbus) before an East to West route finally developed under the Russian expeditions much later. Why wasn't a route established connecting the land masses over the shorter East to West path way first?
Well, there were expeditions to try to find the Northeast Passage - to sail around the north of Russia to get to the Pacific. The Dutch explorer William Barents tried to sail north around Russia in the 16th century, discovered Novaya Zemlya, and died (the Barents Sea is named for him). A couple more expeditions found that the mouth of the Ob River was pretty much as far as you could get before the ocean froze. Unlike the Northwest Passage, there was no labyrinthine maze of islands and channels to keep the hope alive of a navigable route, and interest collapsed.
As for overland through Siberia and across the Bering Strait, the Chukchi peoples who inhabited the peninsula directly across the Bering Strait from Alaska knew that there was some form of land across the strait. However, they were hunter-gatherers, and never bothered to explore that land. Further south, the Japanese had no interest in trying to sail northward and see what was there. That left the job of exploration to the Europeans.
By the time Russia reached the Pacific in 1647, the Americas had already been discovered. Semyon Dezhnev became the first European to sail through the strait in 1648, but it was only in 1732 that Mikhail Gvozdev became the first Russian to sight North America. The first serious expedition to Alaska wasn't until Vitus Bering's expedition in 1741. The expedition went terribly, Bering died, and only a few members of the expedition made it back. The next exploration of Alaska wouldn't happen until Captain Cook.
So yeah, the opportunity just never arose for real discovery in the Northern Pacific. In the Atlantic, it did.