The Ascians certainly didn't give up after the Thirteenth was consumed, so they definitely believed it was possible (whether that was a rational belief or not given their tempering is up in the air of course). The ShB patch cycle has done a lot of building toward a foundation for reclaiming the Thirteenth as well.

There was also the out-of-story pre-ShB marketing from the Fanfests about the Eighth and Final Calamity, so the idea is out there that the Ascians only needed a certain number of Rejoinings to awaken Zodiark, though of course that line hasn't been followed up in the story as far as I'm aware.