To put this in context, Earth has ~3000-4000m evuivalent global ocean.

If Mars were made of an identical mix of stuff as the earth, and equally differentiated, we would expect half this depth, due to the larger surface area to volume ratio of the smaller planet - i.e. 1500-2000m

The 500m that is hypothesised is conveniently equal to this latter value, scaled by the observed D/H ratio which tracks water loss over geologic time by solar wind processes.

Unfortunately, we don't see evidence for an ocean that large on Early Mars. (Remember that water runs downhill, so the northerm plains would have been so full that they would have spilled into the southern highlands, erasing the craters we still see there. So either that water was always frozen, or its duration on the surface was very brief indeed.

The water now seen in the band below 60 south must have arrived by vapour deposition from the atmosphere. Its location is high ground - liquid could only arrive there as rain, and we don't see run-off features that would result from rain hitting the loose soils of Mars.