According to the theory of special relativity, it is not possible for any object with mass, including humans, to travel at the speed of light. As an object with mass approaches the speed of light, its energy requirements become infinite, and its relativistic mass increases to infinity, making it impossible to accelerate to or beyond the speed of light.
However, even if we were to consider a thought experiment where someone could travel at speeds arbitrarily close to the speed of light, there would be no direct evidence to suggest that such travel would allow us to "see the future."
Special relativity does predict the phenomenon of time dilation, which means that as an object approaches the speed of light relative to an observer, time appears to slow down for that object compared to the observer's frame of reference. For example, a hypothetical observer on Earth watching a fast-moving spaceship would perceive time passing more slowly for the spaceship's occupants as the spaceship's speed approaches the speed of light.
But this time dilation effect does not mean that someone traveling near the speed of light would gain access to future events or gain the ability to see into the future. Time dilation is a relative effect, and the person traveling at high speed would experience their own time passing normally from their perspective.
In summary, while special relativity predicts time dilation for objects moving at speeds close to the speed of light, it does not grant the ability to see the future or allow time travel in that sense. The theory of special relativity remains consistent with the principle that causality is preserved, meaning the order of cause and effect events is maintained for all observers, regardless of their relative motion.