Only the northern half or so of European Russia was Finnic, though. And it wasn't even all Baltic Finns, it was mostly Volga Finns. At most you'd get a Finnish version of Novgorod (in terms of territory). The language would be closest to Veps.
Speaking of the Russians, if you could keep them weak and somehow get Finland+Karelia on the level of medieval Sweden, you might have a Finland which could maintain independence from outsiders, assuming it converts to Christianity.
One idea I had thought of is if the Sami domesticate reindeer earlier, and then the Finns to the South adopt reindeer herding as well. It might give them a bit more resilience. And for an even crazier idea, domesticated moose sometime in the first millennium. Combined that would give the Finns more resilience, although their neighbours would probably also adopt it within time thus taking away any advantage. But Finland would be slightly more prosperous.