Godel argued with Einstein the his field equations were solvable with a system that demands the existence of time travel. It's called the Godel metric solution, and is so mathematically sound that Einstein began doubting the robustness of his own theories in attempt to preclude the feasibility of Godel's solution. Not a proof, but an indication that time travel might be possible. We (people) shouldn't assume it's impossible simply because we don't have the theory, math or tech to achieve it.