Whether the Russians knew if it was possible to reach Canada via the Beringer Street depends on what you mean by Russians.If you are about the Russians that we know today then no first yet. The Russians lived in the late Middle Ages/early modern times not beyond the Ural Mountains.
During the 16th century it was then Russia what looked like this:
Spread to the ‘ Siberian front ‘.
This started with Trading Post that was founded beyond the Ural Mountains and with the subjugation of Tatar peoples who were in the way of this trade. This expansion to the east was done under a similar manifesto if the expansion to the West in the United States in the 19th century and the main purposes were therefore economically for the trade in fur. Enlargement was soon after the subjugation of the Tatar peoples. The only peoples who lived there were still in undeveloped tribal societies with the exception of some khanates. Around 1700 the Kosakken (which played the largest role in this colonization) reached Kamchatka.
In the 18th century, Vitas Johassen Bering (a Danish shipping carrier) was appointed by Peter the great to carry out an exploration of Kamchatka and later to determine whether Alaska and Kamchatka belong to the same landmass or that Alaska belongs to America.After that it was clear that this was obvious to America, Peter the great was determined to claim as much country as possible for Russia.
In short, for the Russians of the early modern period, the Beringer Street was not yet known until it was explored by the Dane Vitas Bering Werdt on which Alaska immediately Werdt colonized.
But!If you mean the local Siberian peoples living in the Siberian regions on the Pacific coast.
Firstly, they are not Russians.Then not, not now, never not. If you talk about the real Russian population then you speak about the population in European Russia and the large groups of Russians in the many cities that are located in the (early) modern time in Siberia.
Or the local tribes from the street to Alaska knew not so very well known.There are suspicions and theories about trade contacts between the populations, but here is no significant evidence for it.
You can set that up.Alaska was part of the Russian Empire, until the Russian rulers decided, in 1867, to sell it to the United States.The distance from Moscow to Alaska was so immense and practically impassable, that there was no real effective administration .So then sell it, then you have some.
It is said that the first inhabitants of America have reached that continent via a land bridge where the Bering Strait is now. Those were East Asians….It is said that Russia (much later) was founded by the Vikings.