Associating partners with Allah and blasphemy occurred after prophet Idris (Enoch):

Explanation

Blasphemy occured one thousand years after Adam which was after the death of Idris. The first of the prophets was Adam , then his son Shith and then Idris.

Nuh (Noah) was the first prophet sent to the blasphemers preaching the worship of Allah, the one who has no partners.