Not uncommon in older audio systems, car or home.
Couple of reasons, none that would be worth fixing since it is too cheap to replace the unit.
Coupling-capacitors are often used on the power supply for the pre-amp and amp, if either fail DC voltage builds up and "pops", once powered up all is well.
Music/sound is just vibrations of air, speakers vibrate the air to mimic sounds, amps do this by varying the voltage to the speaker, the "pop" is a varying voltage sent out to the speakers.
I doubt car systems used speaker relays but home systems often do, these delay speaker connection for a few seconds after power up, avoiding the user from hearing the "pop" which is still occurring, lol, but not heard.
Sub-woofer amps almost always have a speaker relay, if it fails you will get a "thump" at power up and then another "thump" about 5 minutes after power is off, lol, doesn't effect sound quality, just annoying.
"Pop" could come from pre-amp or amp, the head unit often has both in a car system, so if you change the head unit no more "pop".
If you have a "premium" sound system it may have a separate amp, so you could get the "pop" even with new head unit if the amp is the part that is "popping".
Ranger radio diagrams here: Ford Ranger Radio Wiring Diagram
Don't see Premium for 1998-2002, but diagrams could just be missing.