If Time Travel would be true throughout the history of human kind, at any point in time whether past or future, time travellers would be "all over us" in telling about the future or past or whatever.
However, there are no stories of either such people or common stories of such being told from one person (the traveller) to another.
Therefore, time travel isn't going to exist ever!
Logic: Modus tollens
If Time Travel then Time Travellers (or common stories of such)
No Time Travellers
No Time Travel
Please remember that:
An assumption that Time Travellers are lying to us all the time is an unreasonable story!
Also, stories of the future would hold a kind of plausibility or coherence so that if the stories would be prevalent then the "Nostradamus" stories would be recorded or a record of place and people would be with us.
The coherence here would be that of our reality entails/is able to hold the story of the future by specific calculations, inventions, a record of history from the future or technology all the way up to that point in time.
A fake story of time travelling will quickly fall apart because it's not coherent with you travelling in time and discovering new histories of science in the future or whatever the "bridged" story that marks a genuine story of time travelling. First, fx., where's your time-travelling UFO? In your garage?