How do I connect ProtoArc Bluetooth keyboard with Mac mini using USB-C cable?

To do the initial setup of the Mac mini, you will need to use a wired USB keyboard and mouse, or if you happen to have the Apple Magic Keyboard and Magic Mouse, you can pair them to the computer by connecting them with the USB charging cable(s) they shipped with.

Connect accessories to your Mac mini - Apple Support

not all wireless device that has an usb-c port can use that port for anything but charging, so connecting them by usb-c to a computer to use them as a wired option may not work.

A current Magic Mouse has the charging port on the bottom:

Not convenient. You can get a rudimentary wired USB mouse almost anywhere for under US$10.

You can use Mouse keys from a Magic keyboard, which will work with a cable:

Use your keyboard like a mouse with Mac - Apple Support