The earliest mentions of the concept I've seen in fiction is probably H.G. Wells' The Time Machine (1895). Did any Ancient Greek philosophers ever bring it up? Maybe some Bronze Age Mesopotamian myths? Who first thought up time travel?
I'm a little sad this didn't get a response, I would also be very interested in answers to this. I also asked it in /r/history just to see if people there can brainstorm some examples.
A possible example from before HG Wells could be Dickens' A Christmas Carol (1843), where Scrooge visits his past and future. It can definitely be argued that he was only being shown visions of the past and future; seeing the future is not the same as time travel. The concept is in there, but Dickens uses words like visions and shadows to describes the future setting.
"You are about to show me shadows of the things that have not happened, but will happen in the time before us,"
"Are these the shadows of the things that Will be, or are they shadows of things that May be, only?"
Edit: Another example is Rip Van Winkle, by Washington Irving 1819. A man from before the American revolution wakes up a generation in the future and returns to his home village to find most of the people he knew are dead, but his children are completely grown up and take him in.