How can I attach a USB microphone to a Breakout-board using ADC Ports?
You can't. The USB "Microphone" is actually a microphone, an amplifier, analog filtering, an ADC of its own, a bit of digital signal processing and a microcontroller that speaks the rather complex USB protocol, probably all in one chip (aside from the actual microphone).

There's no analog signal coming out anywhere of that thing.

You need to use an analog microphone, add your own amplifier and anti-aliasing filter before connecting it to your microcontroller's ADC.