The title of this video wouldn't make sense if it were about any other subject. But the question really is: who first wrote about time travel? The idea could have existed before it was written about, but we would never know. This video looks at what we know about the evolution of time travel as an concept from the writings we have.
Evan Puschak from The Nerdwriter explains that science fiction isn't that old. Literary time travel existed beforehand, even before the technology we associate with time travel, but it was different from what we are used to now. -via Laughing Squid