Log into Mac Mini with unpaired Bluetooth keyboard and mouse

A mac with no USB keyboard or mouse and no Bluetooth keyboard or mouse pairings will automatically go into pairing mode to search for a Bluetooth keyboard & mouse.

I have not tested this with Bluetooth devices defined, but not available -- but from what I'm able to read, it should go into pairing mode if there are no input devices available. If a display is attached, you would see the pairing window open -- so you'll know if this is working.

If it does not, your only option may be to use a USB keyboard & mouse (do you have any friends who have a keyboard & mouse that you can borrow for a few minutes?)

Normally when I do this on a mac, nothing is previously paired. This is how Apple handles non-laptop devices where the owner only uses Bluetooth input devices.