By this truly wonderful invention (exquisitely simple in its machinery, yet of surpassing power) the obstacle of Time is as effectually conquered as that of Space has been for the last generation by the Electric Telegraph; and future years—even, it is anticipated, future centuries—will be made to respond to our call as promptly and completely as do now the uttermost parts of the earth wherewith the magic wire has placed us in communication.
Frances Power Cobbe, Master Traveller
I place Frances Power Cobbe as the author of the first science fiction time travel story given that in her book a scientist invents a machine to retrieve information from the future—certainly an accomplishment worthy of a Master Traveller Citation.
For you allow that, while ghosts out of the future are unheard of, ghosts from the past are not infrequently encountered.
An Eloi Honorable Mention
The hands were whirling around the dial from right to left with inconceivable rapidity. In this whirl we ourselves seemed to be borne along. Eternities seemed to contract into minutes while lifetimes were thrown off at every tick.
Edward Page Mitchell, Master Traveller
In Lost Giants of American Science Fiction, sf historian Sam Moskowitz cites Mitchell as the first to spearhead five important sf themes in his anonymously published, syndicated short stories for the newspapers. One of those themes was the idea of a mechanism (rather than a dream or trance) to take a person back in time, as presented in “The Clock That Went Backward”—the first time machine! Another time travel innovation of Mitchell was the time traveling ghost from the future in “An Uncommon Sort of Spectre,” who unlike Dickens’s ghosts could interact with the time he traveled to.