By conquesring the continent. He wasn't appointed, he took the throne by force.
Well...
Get to work then.

The point is, there's only been one other dragonborn (afaik) that came out of nowhere, like our characters. That was Talos. He didn't start an empire per se. He took the makings of one and defined it further. Alessia's bloodline is the "real" hereditary imperial bloodline. For whatever reason (that I don't know), her bloodline didn't carrry or merged with Reman. Something like that? All I know is that Talos had nothing to do with either, and yet, carried on Alessia's legacy.
edit: It should be mentioned though that the Elder Scroll prophecy says we are the last Dragonborn. So maybe this is all moot. What's the point of leaving any sort of legacy or work, if that's the case. Maybe the whole cliche "mysterious hero who rides off into the sunset" is correct.