James Gunn, the creator of the superhero series Peacemaker and co-head of the DCU, revealed exactly when Season 2 of the series takes place after Superman. Notably, Superman, also helmed by Gunn, is the DCU’s first cinematic entry.

So it seems the DCU show's lates season picks up only a month after the events of Superman. I honestly like the idea of the show not being too far removed from the interdimensional chaos that occurred in that film.