If it was gulf of Bothnia, depending of the exact time-scale, Sámi tribes could inhibit the whole map, excluding the coasts, or only north and east parts, or only north or or...
There are Sámi place names as south as Uusimaa (around Helsinki). I've also read that linguists have concluded that Häme (a region of southern Finland (southern at least from my perspective)) is actually the same root word as sáme [saame, sääme] = sápmi however you spell it. So at some point of history, the inland häme was a sámi region, while the later (more?) finnic tribes claimed the coastal areas.
There are some genetical evidence that the Sámi did not collectively shun north, but rather assimilated into Finns as the settler lifestyle slowly made its way inland.
Now if it was the Arctic ocean, the distribution of more-like-Sámi-than-Finn-tribes would be arguably a majority (at least geographically) rather than minority that it is currently. But it's a fantasy world.
DISCLAIMER: there are some debate historically too (though more evidence of sámi presence in even southernmost Finland seems to pop out every now and then) and it's difficult to say anything on this subject without overly broad strokes, so take the above with a grain of salt. Especially since I haven't posted sources...