Has this particular Google Home Mini been previously set up? If yes, how long did it work as intended before experiencing this issue? Can you see the device in the Google Home app at all to see it's firmware version?
To help find where the issue may be occurring, it'd be useful if you have two devices and use one as a Wi-Fi hotspot. Here's how to do that:
If the speaker still can't connect through the mobile hotspot, the problem is likely with the speaker. If the speaker is able to connect through the mobile Wi-Fi hotspot, the issue is likely more with the settings on your Wi-Fi router.
I wanted to check in and ensure you are good to go, and everything is working properly. Please let me know if you are still having trouble, as I will be locking the thread in 24 hours due to inactivity.
Thanks so much davidking for the helpful replies!