Time dilation, as described by the theory of relativity, can indeed cause differences in the passage of time between different reference frames. However, it's important to note that time dilation does not allow us to "move faster into the future" in the sense of experiencing time at an accelerated rate compared to others.
Time dilation arises due to differences in relative motion or gravitational fields. For example, if one person is traveling at high speeds relative to another person who is at rest, the moving person will experience time dilation, perceiving the time of the stationary person as passing slower. This effect has been confirmed through experiments and is an essential aspect of relativity.
However, it is important to understand that time dilation does not grant us the ability to skip ahead in time or move faster into the future compared to others. From our own perspective, time will always appear to pass at a "normal" rate. Any effects of time dilation would be relative to other observers or reference frames.
In practical terms, time dilation is typically observed in situations involving high speeds, such as in space travel or when considering the effects of gravitational fields near massive objects. While time dilation has real physical consequences and can be accounted for in various scientific applications, it does not provide a means for humanity to leap forward into the future in a way that is perceptible on an individual level.