Amaare found Braxas as a baby during the aftermath of the Calamity, he parked his wrecked ship on the shore, was heading back to check on friends and found this baby Couerl curled up against her dead mother. He picked her up, plopped the half dead from starvation kitten on the top of his head and continued on his way. The scars on his face? Too many facehugs and kisses from Braxas while he was raising her.
A good FFXIV lore site: http://ffxiv.gamerescape.com/wiki/Eorzea