Yeah, no question that it's difficult. Lots of things would have to change and require an almost strategy-player level of focus over generations. But I don't like completely discouraging hypotheticals on principle, because even within the bigger laws of material history there's room for unpredictable events with long-lasting consequences.
Well, as I said before, if Russia stays out of the European mess, preferably starting from non-participation in the 7YW (this also includes no wars with the Ottomans) and makes a dedicated effort to expand on the Far East, building in a process a supporting infrastructure and providing a steady resettlement to the newly accessible Eastern regions starting from the Western Siberia and then further to the East, kicking the Chinese out of the territories which in OTL Russia got only in 1860 to provide a self-sustainable economy of the Russian Far East and after this is done proceeds with the naval development on the Pacific and starts noticeable settlement of the American Pacific coast then they are well-entrenched before the Brits or the rebellious colonists manage to get there in the noticeable numbers.
Is this
completely unrealistic? No, because none of these requirements was physically impossible. However, the probability is quite low and a number of the butterflies is staggering both for Russia and for the whole Europe.
Just as an idle thought (and don't take it too seriously), when these pesky colonists got upset with a request to pay the taxes (something like 3%, IIRC; now I'm paying more just as the
town's taxes and fees

), the British government asked Catherine II for help offering Majorca as payment for the troops. Catherine refused to interfere into the "quarrel between King George and his subjects" but what if she agrees and requests pieces of the American Pacific coast as the payment? At that time the Brits (AFAIK) did not care too much about most of the area so they are agreeing. The open question is how on Earth the Russians would manage to get any noticeable number of the settlers there with their 1st circumnavigation being a matter of the future, the Russian-Chinese border still being one established by the Treaty of Nerchinsk, Siberia having very little of the Russian population, main Russian interests being on the Black Sea coast, etc.? However, this is a
legal opportunity to make a stake recognized by the Brits, Can you fantasize some plausible details?
Edit: Actually, an idea of Catherine's involvement is "borrowed" from the "Трехглавый орел" by Свержин
https://www.e-reading.club/book.php?book=50900
quite entertaining schema because, among other personages, it involves "Tsar Peter Feodorovich" also known as Емелька Пугачев, certain French artillery lieutenant, and .... Баба Яга.
