Using Bluetooth Keyboard with Mac mini at Lock Screen

Hi. Myy wife has started to use a Logitech bluetooth keyboard with her Mac mini. She has the Mac mini password protected. When she switches on her Mac mini (having first switched on the Logitech keyboard) the Lock Screen appears and she is unable to type in her password as the Mac mini does not appear to connect to bluetooth devices at this point.

Are we doing something wrong? Is there a way to force the Mac mini to connect to Bluetooth devices at the initial Lock Screen, so that she can then type in her password?

At the moment, she is having to plug in her old wired Apple keyboard just to get past the Lock Screen then unplug it and put it away, which defeats the object of wanting to use only the bluetooth keyboard.

Any assistance you can give us would be appreciated.

Thanks

Mark