@Lurt One way to answer that is with a resounding yes, since the normal flow of time provides time travel implicitly. In fact, it is the only way time works according to current science. There are mathematical models that provide more flexibility about it, but this mostly applies to the quantum realm and nothing we can actually witness.
A well-proven physical phenomenon that would seem like time travel in our experience is well-proven. Einstein's special and general theories of relativity describe "time dilation." The special theory states that when two objects are in motion but not moving together, and time is measured in both, the measure of time in one object will appear slower to the other object. This effect is so small that it is usually not perceptible, but it becomes greater as the difference in the speed of the two objects approaches the speed of light.
The general theory resolves the paradox of both being slow with respect to one another. When one object changes its velocity and direction to match the the other, the one that changes will remain having a slower clock than the one it caught up with. That will make it seem like it went fast forward through time.
So if you take a trip on a spaceship that travels near the speed of light, and you stay at that high speed for a while, you will see that your clock is behind the Earth's clock when you come back home. So from where you are sitting, you moved forward into the future.
However, you can't go back. There is nothing you can do to reverse the flow and come back to the Earth without all that time staying lost forever.
So the final answer is "yes" - science says it's possible. But if you want to go forward in time like it happens in the movies, you need a very fast spaceship - many thousands of times faster than anything we have now. It is unlikely we would live to see such a thing, but if it happens, astronauts on these ships will not only be space travelers but time travelers. They may take a trip that takes a few short years for them but centuries could go by on Earth. That's a fun concept, and it might happen someday, but no matter what, it's a one-way trip, just like all other experiences of time are.