it seems that the google home mini is powered by usb through a micro usb, if possible get a usb power adapter that can supply 5V 2A to test. Check by doing this is it able to power up normally.
Since you mentioned about operating in a boat, maybe you can configure something like below
Solarpanel USB Output to > micro-usb of Powerbank configure in UPS mode USB output to > micro-usb Google Home Mini
Note: 4 bay bay batteries should be able to hold for some time.......
Batteries 18650 are purchased separately, get reputable models like Panasonic / Sanyo / Sony / Samsung / LG Chemical.
else if your generator is 12V DC output, you can consider this
still i would recommend you to put a power bank in between as in between
12V DC output from generator > 12 to usb 5v module > power bank set to ups mode > google home mini
While the generator is starting, the generator voltage and frequency normally are not stable.
It is recommended to place a powerbank(acts as UPS) between the generator The UPS will condition the input voltage to stable output 5V for your usb devices.