Follow this guide: https://www.ifixit.com/Teardown/Google+Nest+Mini+(2nd+generation)+Teardown/130974

We don't need to privacy invading, un-"hack"-able components in here

Make sure you are getting the desired voltage before you go plugging things in

take components of USB sound card to get the profile a thin as possible

I used this as a wiring guide: https://www.grappendorf.net/tutorials/nerves-pizero-edimax.html

I use 2x 100 ohm resistors, you may want to go with higher values (ie. 1k ohm)

Solder the audio in, audio out and power to the audio amplifier.

Space saving, I soldered straight to the header pins for 5V and Gnd.

Burn the latest Lite image to the SD card and set it up for headless operation, I created a wpa_supplicant.conf file for my home wifi network and created an ssh file to start the ssh daemon by default.

https://www.raspberrypi.org/documentation/configuration/wireless/headless.md

I used this guide: https://nixingaround.blogspot.com/2016/11/raspberry-pi-zero-usb-audio.html

You should probably reboot here.