The answer varies by nation.

First, if you include Russia among the ‘East Asian Nations’ - they did. Alaska was originally a Russian colony (before it was purchased by the US) and Russian settlements ranged as far south as present-day California.

Second, as to Japan - that nation deliberately closed itself off from the outside world as a matter of policy under the Tokugawa Shogunate, just as the colonization of the New World was becoming a big deal. Prior to that closing off, Japan was engaged in a long period of civil war, topped off by a government set on expanding - into Korea and China, in an invasion that ultimately failed. So they were preoccupied and fixated on Asian affairs.

Third, incentive lacked. Japanese were interested in Mexican silver all right, but that was already in the hands of the Spanish. The Alaskan fur trade was in the hands of the Russians. There simply wasn’t a particularly good reason for the Japanese to travel thousands of miles to the coast of North America. Nor was that an easy journey to make.

There were a lot more attractive opportunities closer to home - trade and piracy in the rest of East Asia. Remember that the Europeans had first discovered The Americas in an effort to get to East Asia, and once they did, busily set up colonial ventures of their own there - because of the huge profits to be made.