Depends what you mean with "time traveling". No, i don't believe it's possible the way science fiction shows it.
However, a form of traveling to the future is possible but it's not like the future is predetermined so you can go there. It's more like you slow down the time for you so when you arrive to a certain destination, it feels like you traveled to the future. It's a similar scenario to freezing yourself and waking up 100 years later. It would still feel/look like time travel to you and the "future people" you meet. But instead of freezing yourself to cover a big distance, you use physics to do it faster and relativity will still cause the same result, meaning you will reach your destination 100 years after you took off.
Traveling to the past though, it creates a ton of paradoxes. If you accept it's possible, then you must accept other things along with it, like "it's possible to bring people back from the dead". If you can travel to the past, it means you can interact with people who have been dead for a long time. How exactly is this possible? And how does that feel from the perspective of the people who you just resurrected because you traveled back to their time? Not to mention your past self?
Sure, there is the explanation of "infinite parallel universes" with "unlimited copies of yourself" but i feel like these are concepts that created to solve these paradoxes. I don't believe anything is true.
However, i do believe you can take a peek to the past, without interacting with it. Meaning you can see/hear the past in the same way you can when you watch a movie. Which is something you can easily do right now. Just look at a star in the night sky and what you see is it's past. The further the star is, the older it's image in the sky is. It's possible that a star had died millions of years ago but you can still see it now. That's because the light travels with finite speed and that speed is too slow relative to the size of the universe.
So if you think about it, the light of the past events on Earth is still traveling in space. Every second of it. The images of the dinosaurs or the human history are floating in it right now. So, if we had a way to capture them, it would be like watching our past, which is a form of time traveling i suppose.