As a kid, I never read DC (Why would I? Excelsior!), but I’ve read some DC time-travel comics since then (don’t tell Stan). The earliest DC time travel that I’ve found was in 1942, but as for the big boys, the Caped Crusader and the Boy Wonder got the jump on the Man of Steel by a few months: Batman’s first travel was back to ancient Rome in Batman 24 via hypnosis by Professor Carter Nichols. Here’s a table of notable DC first time-travel experiences that I’ve found through 1969 (after that, everything became time-travel chaos):
OMIGOSH! Now I remember everything! I went to the past in order to prevent Captain Marvel from ever existing! But when I got to the past, all I did was re-live the same events as before! Curses!

Variants

(1)
  1. “DC Comics,” |pending byline|, in Whiz Comics 26, 23 January 1942.