In 1500, Russia (or rather, the Grand Duchy of Moscovy / Moscow) was still west of the Ural mountains. The Russians would spend most of the 1600s into the 1700s conquering their way across Siberia before eventually establishing a colony in Alaska in the 1800s. But the Alaska colony was so far away from the core of Russia society and rather difficult reach since, to get from Moscow to Alaska, you had to travel through the entirety of Siberia first to get to the eastern ports, that it was too expensive to maintain, leading to the sale of the Russian claim to Alaska to the United States.

Now, while the Russians might not have been in a great place to have a long term effect on the Americas, you might be wondering about the indigenous peoples of eastern Siberia - the people who were right next to the Americas in 1500. There is, in fact, a long history of interaction between peoples on both sides of the Bering Strait. In particular Yupik traders traveled back and forth between Siberia and Alaska, trading with the Inupiat near Barrow, Alaska and with Chukchi herders on the Chukotka Peninsula. Both the Inupiat (and by extension the Inuit) and the Yupik, along with the Aleut further south) are all relatively recent arrivals from Siberia; coming to the American Arctic around 5000 years ago (so "recent" in comparison to than Native American peoples further south, who arrived 15-20,000 years ago at least).