This question came up in a seminar today, and I was embarrassed not to be able to give a better answer. I couldn't think of any example from folklore. There are plenty of people who have an enchanted sleep and wake at some point in the far future - something that resembles time travel - but of course they never travel into the past that way. The only way of seeing (and perhaps conversing with) figures from the past is to summon their ghosts, or to visit the underworld.
H. G. Wells came to mind, of course, but neither in the "The Chronic Argonauts" (1888) nor in The Time Machine (1895) does the protagonist travel into the past of his own world. The most he does is to return to the present from his future travels.
It's been said that the first time-travel stories for children are Kipling's Puck of Pook's Hill and Nesbit's The Story of the Amulet, both published in 1906. I'm inclined to award Nesbit the bays here, since Kipling's is really just a particularly fancy and extended example of ghost-summoning. But when Nesbit invented travel into the past for children, no doubt taking a hint from her friend Wells, whom she credits with a name-check, was she also inventing it tout court? I find it hard to believe.
I'm sure the SF buffs here will be able to put me straight.