I was reading a novel set in 1943 where one character makes a joke to the other about superman. There both supposed to be RAF officers in their late 20s
There was a series of very innovative animated shorts by Richard Fleischer that were extremely popular at the cinema (and still are today).
There's also a dream sequence in the 1943 film No Time for Love where Claudette Colbert dreams that Fred MacMurray is a superhero like Superman, which I'm sure wouldn't have happened unless Superman was famous (even though he does a Tarzan yell at the end). It's a really great, largely unknown movie too.
On a related note, Orson Welles wanted to make Batmanin the 1940s. That might have been awesome. (my bad, it was a hoax). And the new animated Batman series got its look from the Fleischer Supermans of the 1940s.