Mac mini clean El Capitan install -- with bluetooth keyboard?
Apple's Bluetooth hardware controllers activate after all of the system's self-tests at boot complete and the EFI firmware loads successfully, which is indicated by the system playing the standard Mac startup sound. It is at this point that the system will accept boot variables, either stored in the PRAM or those being sent via keyboard inputs. These are then passed to the OS X kernel to invoke the desired startup sequence.

If any inputs are being sent via the Bluetooth keyboard before the controllers are active, then they will not be recognized by the system. However, if these inputs are performed after the controllers are activated, then they will be properly read. Therefore, for Bluetooth keyboards, be sure to press the desired key sequences after you hear the boot chimes and not before.

This does all assume the keyboard has previously been paired with your Mac. If this is not the case, boot into the existing OS and pair the keyboard first.