The lorebook "history of the Sixth Astral Era" section (p.38) just says that "not long after Midgardsormr's demise [...] Eorzea's beast tribes started summoning their own gods - the 'primals' - into the corporeal realm".

The chronology (p.53) doesn't mention any primals prior to Titan, Leviathan and Garuda in 1562. (Small possibility: Nidhogg awoke for a period in 1557 - as referenced in the ARR dragoon quests - which could be mistakenly reported as primal activity. How much do the Garleans know about dragons?)

The Garlean history section (p.177) says that the campain to capture Doma lasted from 1528-1552, and at some point in this period Solus "first laid eyes upon the ruin wrought by primals - an entire land utterly drained of life."