At startup my Mac mini show a lock and later a question mark

A Lock like in the image below ?

If Yes, this is a Firmware Password Lock

Suggest the User reads the details of what it is and what can be done to resolve this issue

Set a firmware password on your Mac - Apple Support (CA)

This means that your Mac is unable to locate an operating system that is functional. It has been erased or damaged. Try reinstalling the OS by restarting the Mac in the Internet Recovery Mode. Hold down the Command + Command + R keys on restart. That will enable you to reinstall the original OS that came with the computer. If you had a newer version previously installed, that installation will then have to be upgraded. If this doesn't work then you likely have a failing computer.

A cable will save you time doing internet recovery, if available. Ethernet is very often "faster" (more bandwidth) than WiFi.