My Mac mini is stuck with an exclamation mark on top of a globe

If you are trying to startup in macOS Internet Recovery Mode?

Try connecting the Mac Mini directly to your Router using an Ethernet cable.

For more info, see > https://support.apple.com/en-us/HT201314#internet

What year model is your Mac Mini?

It is not clear why are you trying to startup in internet recovery mode?

See if your Mac Mini will startup in Safe Made, as per > https://support.apple.com/en-us/HT201262

Check this link:

https://support.apple.com/en-us/HT204156

Ah OK, then you needed to follow the steps at > https://support.apple.com/en-us/HT201065