How old is the concept of time travel? Would the concept have even been coherent to premodern peoples, or is it primarily a cultural artefact of the industrial and space eras?
I ask because I noticed that in the mythologies/folklore I am aware of, there are all kinds of supernatural powers, but I can't recall time travel being one of them.
As far as the folklore of various people is concerned, I know of no pre-modern culture that had the concept of time travel. That said, no one's knowledge of world cultures is comprehensive, myself included. It would be interesting to ask that half of your question - the part about culture (but not the one about the history of literature) - of /r/Askanthropology.