Hard or sudden voltage on a signal wire for the amp turn on can cause speakers to pop.
I’ve had speakers pop when signal cables are broken, in some way. The sudden connection of a dysfunctional or broken wire has caused popping before, for me.
If the car is completely off when this happens, it sounds like a power supply issue, where the vehicle’s amplifiers(s) are being turned on and off or partially on/off in some fashion. I would check the wiring to whateve is causing the popping and like was said above, check the relay and fuses. Anything that has to do with the amp getting power and a turn on signal.