Mac Mini cannot get past startup disk page

Sounds the Mac mini's internal drive is not erased and formatted correctly.

Erase and Format, as per > Use Disk Utility to erase a Mac with Apple silicon - Apple Support

Then reinstall the macOS, as per > How to reinstall macOS - Apple Support

After performing a clean install, but before restoring from a backup......does it boot to the Setup Assistant of the new OS? If not, then you will need to perform a DFU Firmware Restore which resets the security enclave chip, system firmware, internal SSD, and pushes a clean version of macOS onto the internal SSD. You could try just a DFU firmware Revive which should affect the internal SSD and leave the existing OS intact. This process does require access to another Mac running macOS 15.x Sequoia (at this time).

How to revive or restore Mac firmware - Apple Support

If after a clean install you are presented with Setup Assistant, then perhaps when you restore from a backup you are bringing the problem back. Try to restore from a backup, but omit the Applications and manually reinstall the apps.

Startup in Recovery Mode and go to Disk Utility.

In Disk Utility select “Show All” in the small square box.

Then select the whole Internal Drive and click Erase.

At this step, name Macintosh HD set partition scheme to GUID Partition Map and the format to APFS.

Then go back to Install macOS and install Mac OS on the Macintosh HD.

den.thed wrote:

In Disk Utility select “Show All” in the small square box.

Then select the whole Internal Drive and click Erase.

That may not be a good idea. There are two hidden APFS Containers on the internal SSD of the M-series Macs which are required for booting the system even into the Startup Options screen. I am not sure if Apple now prevents them from being erased now or not, but I think early on they would be destroyed. If that happens, then a DFU Firmware Restore is required which requires access to another Mac (at this time the other host Mac must be running macOS 15.x Sequoia).