Impossibility is irrelevant to this thread.

High-speed "relativistic" travel allows little time to pass for the ship, but still means that centuries can go by for the rest of the universe PER TRIP.

If the whole ship could be made to interact with the rest of the world as if it were a single particle or get all of its particles to move in parallel instead of in random directions, that would open up two possibilities: one is moving at very high fractions of c (and possibly having large-scale uncertainty apply), and the other involves the mathematical oddity known as tachions. They're not actual particles as far as we know, but the equations of relativity have solutions that would involve matter moving faster than light and unable to slow down as slow as light speed. (That could be a challenge for navigation if a ship acted that way; the equivalent of normal matter going really slow like we and our rockets do would be instead going so many times faster than light that it's hard to stop at the right time to control where you end up!)

If space is thought of as being made up of pieces of one Planck length and time as passing in units of one Planck time, instead of both being smooth, then you can only move one distance unit per time unit, which is c... but the trick is to figure out which pieces of space are connected to which others (and thus can be moved to in one tick of the clock) and which ones are not. So, although I have no idea how to do this, making one Planck bit of space detach from its neighbor and attach to another somewhere else which seems farther away would make travel at light speed from one point to the other appear to have bypassed other points along the way...