By nature they couldn't know, as nobody had been in the area and mapped it. The idea of the Northeast and Northwest passages hinged on a whole slew of assumptions, most of them related to the lack of skill in determining longitudes - Asia was assumed to be much short than it was for instance, and the idea that Asia and America were as close as they were at the top didn't really occur to people who only knew the Pacific from southern latitudes. When Cortés explored the Pacific Coast of Mexico in the 1520'es he searched for the Northwest Passage form the other end, and believed he had found it in the bay of Baja California, as he though California to be an island. When Vitus Bering was sent on an expedition in 1728 by Peter the Great, the main objective was finding out if America and Asia were connected, as the size of both continents was clear to people at this point.

tl;dr Nobody actually knew that the NW passage existed, but they had from early on very little reason to believe it did not.