One of these: https://www.apple.com/shop/product/MYH93ZM/A/thunderbolt-3-usb-c-till-thunderbolt-2-adapterWhat cables do I need to make this happen, I suspect there should be a thunderbolt cable coming from the display, then you need the converter you speak of which takes it to the Mac Mini M4 ( I Have this model too ).?
The display indeed has a cable built in.