"Time Travel" won't be possible, ever. Primarily because time does not really exist, only "now"... We perceive a "flow of time" only because we can "remember the past" in various ways, and because we can project our thoughts into (plan for) "the future."
In a Universe where "time travel" is possible, every "now" that has ever happened (past or future) must already have happened, with each separate "now" forever existing in some strange "frozen" state, to which a "time traveler" could then presumably navigate back and forth...
This (a completely predetermined and never-changing Universe, with no free will) should be enough to convince you that you can forget about "time travel"...