If the popping sound comes from the speakers, then you are getting a DC transient from the amplifier. Yes, it can damage the speakers, depending on the voltage.
Disconnect the speakers, place DMM probes on the + and - terminals. Set it to read VDC. Turn on the amp and note the voltage (it will go by quickly). If it jumps to over a volt, it can cause problems. But leave the probes there for a few minutes. If the DC offset drops below 50 millivolts (or better yet to a few millivolts), that is the amp showing its age. What you can do is disconnect the positive speaker cable prior to a cold start and then connect it after five minutes or however long it takes for the voltage to drop.
The problem can be caused by many things, but input differential transistors going out of mismatch is the most common, followed by fading resistors in the feedback and/or input impedance. Also a problem is an electrolytic capacitor in the feedback divider leaking or having a high ESR.