Antarctica has four resources, cold, fish, wind, and minerals.
Cold gets you polar salts, the frigid equivalent of solar salts. Potassium and magnesium minerals and salt.
Fish you know about.
Wind power is sort of potential. Lots of icing in that environment.
Minerals is the wild card.
Spitzberg is the precedent I am thinking about. Norway administers the island but anyone can start mining. Coal is pretty much all they do. Norway is attempting to claim the oil for itself but the Russians are ignoring their attempt. An American businessman named Longyear was the first guy to start mining coal and the town of Longyearbyen is named for him. In OTL that was in 1906, but the idea could have been suggested before that, and god knows it's the most sensible arrangement for someplace like Antarctica.
So let's assume someone finds something. Gold, with coal being mined for power for the mines and processing plant. Maybe the Germans are looking for gold to pay the WWI reparations with, like Claude's scheme to mine sea water. Claude was the guy that invented Neon lights.
Then maybe in the thirties a bunch of Jewish refugees move in because of the Bolsheviks in Russia and then the Nazis in Germany.
Now what?