Typical LED indicator consist of resistor (R2) and LED, connected in series with a switch.  When the switch is closing or opening, a glitch noise may occur at the supply line. To avoid this noise, R2 and C1 are added to the indicator circuit and value of R1 is adjusted.

Eliminating LED Pop Click Noise circuit schematic

Very slightly delay is provided by the R2-C1 circuit which is used to prevents the pop sound, but the LED still lights up fast enough that the eye cannot see the delay. The question is, why not just add the C1 capacitor and not have R1 in the circuit? The current in the LED is limited by the 390 ohm resistor when C1 dumps its charge as the switch is toggled. These spikes can cause the life of the LED become shorter even cause it to burn out.

To give the proper brightness with the LED that is being used, the value of R2 should first be selected. You can increase the value of C1 to 22uF or even 47uF as needed if the LED indicator circuit is still causing a pop in the audio.