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 &amp; 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 &amp; mouse (do you have any friends who have a keyboard &amp; 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.