Mac Mini won't open Startup Manager
It’s possible that your Windows-specific keyboard isn’t sending the correct keycode for the Option (Alt) key. To rule out hardware damage, have you confirmed that the Alt key works when booted into Windows or plugged into a different computer?
A workaround is to open the Mac Mini, disconnect the hard drive, and attach a USB flash drive containing a macOS installer (How to create a bootable installer for macOS). You’d still need a way to install onto the hard drive, which means buying an external USB enclosure for the internal drive... I think it’s just easier to try an Apple keyboard.