The distance doesn't dilate; time does. The distance contracts.
E.g., to a photon moving at 1c, the whole universe has a contracted length of 0 meters, and it crosses the whole universe instantly. To us, observers at <1c, the whole universe has a non-contracted length of <a lot> and the photon takes <a long time> to cross the whole universe. By the time the photon's 0-second journey across the entire universe has finished (whatever that means), we're all extremely old. :D This is the time dilation meme of slowly-aging space travelers but taken to the extreme.
E.g., to a photon moving at 1c, the whole universe has a contracted length of 0 meters, and it crosses the whole universe instantly. To us, observers at <1c, the whole universe has a non-contracted length of <a lot> and the photon takes <a long time> to cross the whole universe. By the time the photon's 0-second journey across the entire universe has finished (whatever that means), we're all extremely old. :D This is the time dilation meme of slowly-aging space travelers but taken to the extreme.