I can confirm that the Google Home Mini works with a simple micro USB input, just like a smartphone. The plug is a bit recessed so not all USB cables will be compatible, but I easily found one that is.
You should get a high quality cable because the voltage drop at full volume is enough to make the Home Mini reboot.
The included AC adapter is rated at 5V and up to 1.8A, so get an USB adapter rated at 1.8 or more amps.