Microphone gain with LM386
Here is the schematic of an LM386 board that appears to be the same as yours:-



The gain control trimpot is connected directly to the input with no coupling capacitor, so any voltage on the input will affect the amplifier's DC operating point. If your board has a similar circuit then you need to add a capacitor between the mic and amp input to block DC voltage.

The combination of this coupling capacitor and the 10k pot form a high-pass filter that rolls off below $$\frac{1}{2\pi RC}$$ 

A 0.22uF coupling capacitor would be large enough to pass frequencies above 72Hz with minimal attenuation.