(My answer to this question at Quora.com)
They did. They weren’t “Russians”, as such (a term and a nation that has only existed for around a thousand years), but ancient Siberian inhabitants who crossed into North America, via the Bering Straits and Alaska, and whom we now know as “Native Americans” (in the US), “First Nations” (in Canada), or just “Amerindians”.
Until recently, it was thought that the first such migration occurred approximately 15,000 years ago, but more recent studies indicate that the first arrivals were 8,000 years before that. You can read about it at