We experience time as a one-way street. Within spacetime, we experience four dimensions: three spatial and one forward time dimension. Einstein’s theories show time can bend under gravity, and jumping into the future is likely possible. So, yes, time travel in that sense is possible, and proven. However, that’s not what most people are asking. The key question is can we travel back in time, and that appears to be impossible. Traveling to the past remains a paradox in physics, wrapped in the mysteries of spacetime.
So far, observations show that spacetime only bends in ways that preserve causality.
From a philosophical viewpoint, the interesting thing is that if it is possible, it is possible now. The needed materials and ideas are in the universe now, awaiting our discovery. To push the boundaries of this idea a bit, some solutions to Einstein’s general relativity equations suggest closed time-like curves, enabling travel through time. Despite these philosophical and speculative notions, most scholars say no, traveling back in time is not possible. It appears the laws of physics do not permit time travel to the past, and none of our observations to date support the idea.