How can I check if a new hard disk is detected by Mac EFI at boot?
There is no specific way to get into BIOS/EFI easily on the Mac. It is possible to get into NVRAM from boot and from a shell (type man nvram) but I am unsure you will be able to do anything there that will have an effect on the new drive.

PC manufacturers give access to this because they don't make the operating system. Apple does not because it's software and hardware are better integrated. So if Disk Utility does not see the drive then there is a problem. Possibly with the cabling, my thought being that adding a drive to a mini is a bit finicky.

You could try zapping the PRAM (COMMAND OPTION P R at boot, wait for a second bong then release those keys). I would be tempted to check the connections and cables and even try the new drive in an external (known good) case to verify the drive is OK