In march 1939 the Czechoslovakian leaders were forced by Hitler to sign a document which made Germany a protection keeping force in Czecho. Slovakia was also forced with pressure to declare independence from Czecho. Then german troops occupied Czechoslovakia with hardly firing one shot. This was an illegal occupation and broke the Munich treaty of 1938 but no war.
There were protests and notes from the allies but I wonder if somebody in the U.S. would have recognized this as a war.

The only war related hardly to the saying of the woman in the movie (with german subs playing a role) could be the spanish civil war, but this ended 1st April 1939.

Dirk