I would temporarily get a second 12 volt battery of any size, even a gell cell out of a UPS or 12 volt power tool pack, and use this second battery to power the new radio with the intermittent “pop” problem.

This isolates the new radio from the old car electrical system and helps you narrow down whether the problem is in the new radio wiring or elsewhere.

I would run the new radio with the second battery at rest first to see if with nearly no vibration the problem still occurs. Then recharge the second battery and go for ride over increasingly rough roads.