If Semyon Dezhnev had crossed the Bering Strait in 1654 and discovered Alaska then, Russia would have been well on the way to taking over a huge portion of North America--perhaps the North all the way to Hudson's Bay. The cossack method of occupying new territory was in some ways, much more effective than a joint stock company 120 years later. Dezhnev could have discoverd that the Kobuk Innuit were far more friendly than the Chukchi, gone up the Kobuk looking for more furs (which Alaska has in aboundance) to portage to the Koyakuk and then the Yukon. Someone else would travel down the Yukon to it's mouth and then up to the Porcupine River and portage from the Porcupine to the Deh Cho (Mackenzie). Then up the Deh to what we call Great Slave Lake and then the Smith River and from here, Lake Atabasca, Cochrane and Beaver to the Churchill and Hudson's Bay. Easier than getting from the Lena to the Kobuk, actually.
Then follow the mainstream of the Yukon to the Liard and up the Liard, down the Ketchika, up the Peace, up the Fraser, then either up or down the Columbia, and reach either the mouth of the Columbia or cross the mountains to the Missouri. Then across the Great Plains, meeting the French somewhere between St. Louis and the Great Lakes depending on how long it takes to explore across North America. Estabish a yasak system and missionaries and that's how the Russians take over much of the American West by at least 1800.