From the photo, it looks like Q6 (between the output power transistors) has a crack in it??
The relay is probably connected to a circuit that senses the DC voltage on the output & only turns one once that settles, so there will be no DC or "thump" through the speaker.
It may also be held off by excess current sensed across the emitter resistors, as overload protection.
The relay is not the problem, the control circuit for that is detecting the amp it not in a safe state so keeping the speaker isolated from it, to prevent further damage.