On power on all capacitors are charged and therefore the output of the power stage generates huge surge, which goes straight to speakers and you hear this surge as loud "click".
"MUTE" function is performed within pre-amplifier and that is the reason you will hear this "CLICK" with mute on and off.
Some amplifiers use "power-on" deley relays to protect speakers and power amplifier. This means that the speakers are conected to the output of the power stage after seconds .. when the amplifier achieves stabile state ..
"soft mute” = ramping the volume down/up to mute/100%
Regards,
IanP