Not quite T1 - [spoilers below!]
... spoiler warning again! ...
the first catalyst (Curd of Ages) drops from dungeon bosses at area level 3+ with a 20% chance. The higher-tier catalysts need stronger bosses: Essence of Terroir from level 5+ (15% chance), and Heart of the Land from level 7+ (8% chance). So you'll want to push into mid-tier dungeons to start finding them. Each tier of affinage requires the next catalyst up, so you upgrade sequentially.