c. 1500, "to beget" (offspring), a back-formation from generation or else from Latin generatus, past participle of generare "to beget, produce," from genus "race, kind" (from PIE root *gene- "give birth, beget," with derivatives referring to procreation and familial and tribal groups). In reference to natural forces, conditions, substances, etc., from 1560s. Related: Generated; generating.
word-forming element making adjectives from verbs, meaning "pertaining to, tending to; doing, serving to do," in some cases from Old French -if, but usually directly from Latin adjectival suffix -ivus (source also of Italian and Spanish -ivo). In some words borrowed from French at an early date it has been reduced to -y (as in hasty, tardy).
<a href="https://www.etymonline.com/word/generative">Etymology of generative by etymonline</a>
Harper, D. (n.d.). Etymology of generative. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/generative