Have the 'White Finns' falter during the Finnish Civil War, resulting in a socialist republic being proclaimed in Finland proper.
Ignoring for a moment the unlikely triumph of the Red Guard workers' militia/'Red Finns', have socialist Finland either be heavily influenced by the Bolshevik government and/or have Finland merge with the young Soviet state voluntarily and after having been offered numerous concessions to convince the new Finnish government to join. (i.e. significant regional autonomy, if not some degree of independence from Moscow)
Or, alternatively have the Red Army during the Finnish Winter War experience a total victory over Finland. Finland's forcible annexation follows. Ignoring the purges, have the Red Army do better in the war.
afterwards, have Sweden and Norway become heavily influenced by the Soviets.
In my TL, Finland remains independent from it's Soviet neighbor (the Winter War doesn't occur in this TL btw). By the 1950's with WWII having been fought between an enlarged USSR (which spans from Vladivostok in the east to Berlin in the west) and a fascist or at least nominally fascist France/Italy/Great Britain alliance, Finland is considerably influenced by the Soviets.
So in a way, Finland still finds itself under the domination of the Soviets in my TL to a certain (limited) extent. [laughs evilly]