Popping is almost always due to a sudden change in voltage.
On some of my pedals, this might be because a cap has to charge or discharge before equilibrium is achieved. Occasionally, a pull down resistor might help force such a cap to be in a better state when I next switch the pedal on. Or maybe not. Sometimes pedal ventriloquism comes into play where something in one pedal has no effect on that pedal popping but, by god, does it mess with another in the chain! And that one was totally silent before.
I’ve seen the blame layed with LED’s, caps, low quality switches, duff wiring and the altitude of the moon but I’ve not yet come across a buffer circuit as a cure all.
If your circuit is only popping first time you switch it, I’d imagine that a cap is charging and, once charged, everything goes quiet. I have such a pedal. But it only behaves that way when 2 other specific pedals are in the same chain.
Your boss pedals use a switching circuit that may mute the signal (very briefly) while the switching occurs. Hence, no pop. They may be buffered bypass but it’s not the buffer that makes it quiet