Okay:
1. Have Dezhnev's charts make it to some colonial governor, prompting a 17th. c. atempt at crossing the Bering Straits
2. Have someone else in charge of the initial expeditions to Dauria, obtsaining grain from the Daurs through trade instead of driving them out and precipitating the later clash with Jurchens and Korea,
..
minor pod: Leave the fort in Chukotka to rot, and offer a trade/protectorate instead of endless slaughter on both sides. That should free up a alot of resources to have the Cossacks go explore the Aleutian islands and eventually Alaska.
Those are your "earlier discovery" setups.
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Now...manpower (18th c. onwards) is actually not that terribly difficult: just have a government that
wants settlement and is willing to let serfs be sold to the American settlement project. They will never outnumber the British but they just might be too many to dislodge completely (a-la the French on the other coast).
This requires seizing a good agricultural area. So British Columbia/Washington's Salish lands, or the Columbia river, or beter yet SF Bay (though that could be done later when Spain is weak).
In the late colonial period allow/import foreigners. Probably Chinese. Voila. Once the gold rush starts that should be easy enough (Yukon, Alaska, BC, Columbia basin and California all being *russophone).
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Now this Russian America might still get conquered, but it will retain a distinct cultural setup.
There you go.