For a distant yet stationary observer of space travel, time or the progression of clock time slows, called time dilation, essentially due to the doppler effect upon light.
For the traveling astronaut speeding along close to the speed of light, distances and time of travel are actually shortened due to the astronaut's own speed. Everything is normal. Our astronaut will indeed reach his final destination long before this fact is recognized by any distant stationary observer of the traveling astronaut.
From light's point of view
the entire journey from planet A to planet B took no time at all since all distances in the entire universe has been at zero length and therefore both planets A and B are situated at exactly the same location!
Another way of saying this, but in considerably more erudite fashion ( i.e., not easy!! ), is that for
'Lightlike Space Intervals'
only a light pulse can be present spatially and temporally ( time - wise ) at two events simultaneously. And this can only occur on the surface of the light sphere given by Minkowski-Bondi pseudo Euclidean geometry. That is, the proper time interval on the surface of a light sphere
occurs between the transmission and reception of a light pulse which, by the physics of the light sphere, is zero.