Or is it byproduct of general relativity.
As far as I know, no notion of time travel before Herman Weyl's 1922 book "Space, time, matter", where he vaguely discusses the notion that the metric of spacetime could become so twisted as to allow time travel. I recall a 1917 special relativity book discussing the classical problem of a particle going faster than light going backward in time, but only to underline the notion being nonsensical (the first articles on tachyons arrived in the early 70's or so). The only other notion that could relate to time travel before those is advanced potentials (solutions of the wave equation which might be interpreted as going backward in time after being emitted), this too was not discussed that much, except around in the 40's for the Feynman Wheeler absorber theory.
If you want some old timey discussion on advanced potentials, check out W. Ritz's 1908 article, "Recherche sur l'électrodynamique générale", where he discusses time symmetry in the Maxwell equations. I think Hugo Tetrode's 1922 "Über den Wirkungszusammenhang der Welt. Eine Erweiterung der Klassischen Dynamik" is supposed to be also similar but I cannot read German unfortunately.