Fayths existed before the Fayth Spring. Zanarkand was after all, the city of Summoners.

Me and Duality (artist formerly known as Aurons Ghost) still debate till today if any of the 9 Fayth (Valefor, Ifrit, Ixion, Bahamut, Shiva, Yojimbo, 3 Magus Sisters) were made before or after the Zanarkand / Bevelle war.

We know Anima was made 10-15 years prior to X by Yunalesca. We know that because (SPOILER)Anima's fayth is Seymour's late mother