I really just want to know at what point must the rampage inducer become active, whether it should be at any time before round 55 or at the very start of the game before killing anyone.

Just turn rampage on at any point in the run and its a rampage run

I mean I would assume for a run to be counted as a rampage speedrun that rampage should be activated on round 1 (ideally before getting any kills) and remain on for the duration of the match.