I would try the restore options first. You can find instructions for the restore menu here

If the recovery menu doesn’t work put the Mac mini in DFU mode by following the instructions I have here

One the device is in DFU open Apple Configurator 2 (Mac Only sorry Windows folks). Make sure you are at least at version Version 2.13.2

Connect the USB-C cable to the Mac and the Mac mini to the port closest to the ethernet port

If you are presented with the DFU screen below in Apple Configurator 2 the procedure was done correctly

Right click -> Advanced -> Revive device

This will download the operating system and perform a reinstall of the OS preserving the user data

If you would like to erase everything pick the restore option

Apple Configurator 2 will go through downloading the firmware and perform a restore of the system

1. Disconnect the power cord from the Mac Mini.
2. Plug USB-C/Thunderbolt cable into the USB-C port next to the ethernet port.
3. Plug the other end into the Host Mac.
4. While holding down the power button, connect the Mac Mini to power and continue to hold the power button for about 3-5 seconds
5. You should now see the DFU logo on the Host Mac.

I recently purchased one of the newer Mac mini devices with the new M1 chipset. Unfortunately I went with the lower edition that had 256 GB and I wanted to send it back to purchase the bigger 512 GB edition, but I wanted to clean my installation.

In order to to boot in the recovery mode to reinstall the os I had to perform the following steps:

1. Make sure the Mac mini is off, if its not off just shut it off
2. Hold the power button until the options appear, it might seem like a long time but keep holding it. It took about 15 seconds for me.
3. A menu should appear that shows the hard drive and Options. Select options and continue
4. You will see the apple logo and then a new menu should appear with additional options. It would look like this:

5. If you want to perform a clean install go to Disk Utility first and erase the current partitions, after that step is complete come back to the options screen and Select Reinstall macOS Big Sur and click on continue