Noah didn't remain in the Rumbling Region. The guilds that Chief Ash had sent away knew that he was there, and the Crystal City didn't withdraw the bounty.
More mercenaries and assassins would come for him, so he couldn't remain in the same place to train. It was better to find a different spot far away from the Rumbling Region where he could spend peaceful years and focus on his prowess.
Noah had maps and Soul Stones to spend in case he ran out of ideas. Finding a safe spot inside the Hellish Landscape wasn't a problem with so many forces occupying its territories.
Noah eventually opted to avoid any interaction with the human forces and travel through the vast sea of flames until he found a spot far away from any recorded inheritance. Fire in the middle tier couldn't hurt him anymore, so he had many options at his disposal.