We also don't know when that ship arrived on the moon. It might have been up there since before the fall of the Empire -- or it could be very recent, maybe launched there from Dalamud when it started falling. It's even entirely possible that it's how we get to the moon in the first place -- we could hastily jury-rig a scavenged ship because we need to get to the moon very fast for some reason, and end up crashing it there as our starting point into Mare Lamentorum. There are plenty of different possibilities. It's clear that it would have been possible for the Allagans to get to the moon -- Dalamud itself would probably be enough evidence of that -- but the history of this particular ship has yet to be told.
