Hi @cambodan
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
https://www.ebay.com/itm/Black-PowerBank-Soshine-E4S-LCD-Display-18650-Battery-Charger-Mobile-Power-Bank/182970636486?hash=item2a99e658c6:g:iHMAAOSwU4FaN-4Z
https://www.ebay.com/itm/Soshine-LCD-4-Slots-18650-Battery-External-Charger-Holder-Box-with-Dual-USB-I3C0/302117658778?var=600934772790&epid=2142952458&hash=item46579da09a:g:1mcAAOSw44BYDrvP
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
https://www.ebay.com/itm/DC-12V-to-USB-5V-3A-15W-Converter-Regulator-Step-Down-for-Car-GPS-iPhone-Samsung/142625731712?hash=item213527f480:g:0S8AAOSw7qdZ6G7m
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.