Is a 30” Cinema HD monitor compatible with a Mini Mac?

You need a USB-C to Dual-Link DVI adapter.

https://www.startech.com/en-us/audio-video-products/cdp2dvidp

The Apple display has an attached cable with a male Dual-Link DVI connector.

Hi, welcome to the Apple Users Community.

It's very likely but with such limited information on your Mac Mini and the display, we would be guessing.

Help us to help you by letting us know more about the specs and age of the units.

Best of luck

Most of these are USB-C to female Dual-link DVI adapter, and unless the OP has an existing dual-link DVI M/M cable with the 30 inch Cinema Display that can plug into the adapter, then that will be another cable expense.

The display has a cable with DVI, USB, FireWire, and power plugs.

The DVI plug goes into the USB-C to Dual-Livk DVI adapter that plugs into one iof the com;puter's USB-C/Thunderbolt 3 ports.

The USB-A plug goes into the USB-A port on the computer.

The FireWire plug is not used

The power plug goes into the display's power supply unit.

https://www.amazon.com/Odyson-Supply-Replacement-Cinema-Display/dp/B01N7KWQAL

Thanks for clearing that up. Before I posted, I attempted to find that detail information, or an image that showed the cabling. Probably knew this in 2004, but had forgotten.