Some White force of some relevance sets up shop there during the Russian Civil War with enough Japanese and American backing that the Soviets don't bother retaking it. It's quite like a Russian "Taiwan" of sorts, but it remains remote and distinct enough that in the end Moscow lets it be. This probably requires Kamchatka NOT being actually hosting a Romanov and quietly dropping any pretense to be "Russia", i.e. just be willing to be left alone. This is rather unlikely for a White Russian force, but you can imagine a rapid influx of Japanese and/or Americans, or maybe the White troops originally involved happen to be majority non-Russian (mostly Baltic German officers with largely Caucasian troops, say? A pretty bizarre happenstance, but in the chaos of the times, perhaps possible) and thus by the thirties the place has a majority uninterested in claiming a non-Soviet Russian identity.
Assuming a butterfly trap, WWI begins roughly on schedule, though Kamchatka is clearly going to be a sticking point between the Soviets, the US and the Japanese that may affect the East Asian theatre. However, let's go for minimal changes: alignments occur like OTL, perhaps the Soviet/Japanese conflict begins earlier (which would have important ramifications later on) but anyway the Kamchatkan government sees where the wind is blowing early and picks America over Japan when hostilities erupt between the two (were they to join the Axis in some capacity, they would be reintegrated into the SU afterwards). Then, they are a minor, but independent Ally, fighting the Japanese alongside the Americans and the Soviets. They are rewarded with continued survival, and they either essentially become a Far Eastern equivalent of Austria in the Cold War (neutral) by switching Japanese protection with the Soviet one, or join one bloc: if they join the Soviet bloc they are likely to become a SSR however, so more likely they become a frontline Western ally, basically somewhat of a colder South Korea (Korea is probably wholly Communist ITTL btw). Notably, this country probably includes most or all the Kurilis too.
All of this requires luck and in not very likely, but it's the best I can do.