If time travel was real we would all be aware of it and it would be an ordinary everyday thing we all would use.

Think about it...

At first it would be a secret invention. But as time passes, more people are "let in on it", then it gets tweaked with and upgraded. Maybe only certain people would know about it and use it. But after time, it would get out and eventually mainstream. Once everyone had access there would be so many people going back and forth that we would all see people of the future and after some shock and dismay people would get used to it and it would be just as normal as using cars, smart phones, and indoor plumbing.

Even if it was not invented until the year 3025, people would travel as far back as when man was first on the planet. And as early as man could comprehend that the tech is possible they would become part of the travelers.