The Russians did find Alaska. Perhaps the first explorer to see Alaska might have been Semyon Dezhnev in 1648. He was in the area and may have either run across the Alaskan mainland or nearby islands. It's disputed exactly what he found.

The settlement and exploration of Siberia was a long and extremely difficult endeavor. As of the 1690s they were still exploring the Kamchatka Peninsula. Petropavlovsk-Kamchatsky, the first major Russian settlement on the East Coast, wasn't even settled until 1740. So there weren't really any fishermen or traders to be out wandering about. Prior to that the only sea access was at Okhotsk (on the Sea of Okhotsk), which is a good 2200 miles from Kodiak in a straight line, and nearly twice as far by sea. With Kamchatka, the Kuril Islands, and Japan in the way it'd be hard for someone to accidentally hit Alaska without hitting one of them instead. Until Petropavlovsk was established there wasn't a Russian settlement directly on the Pacific. Do there weren't any Russians in the area to accidentally discover Alaska before then.

From 1733 to 1743 the Russians conducted a series of voyages in the area to map and claim what territory they could. This is now known as the Great Northern Expedition. It was a follow up on exploration missions in the 1720s that explored the Russian side of the Bering Strait. In 1741 one of these voyages set out from the newly founded Petropavlovsk and discovered Alaska. Even with royal funding about half the men on the voyage died, and half the ships were destroyed. The Bering Strait was a deadly environment to explore. Even Vitus Bering left his bones there.

Of course the native peoples like the Yupiks knew about about the land and settled on both sides of the Strait.

/u/The_Alaskan might be able to provide a more thorough answer. But I think that more or less covers the basics.