Custom Cable Prototype and Manufacture
The fact that is it USB-C is what makes it specialized. If you're not opposed to an internal connector, why not fit a USB-C socket on your board to allow for cheaper USB-C to USB-C cables?

Getting past that, you're after a cabling loom manufacturer. However, to make good USB-C cables it gets much harder than one that crimps and plugs looms for you. Your best starting point may actually be with your PCB / Assembly vendor, as they will have had to handle similar things, with most having the option of basically designing your product from scratch.

If you want a lead on a more local to you option, giving hints of what country you're from will help narrow it down.

Equally, contacting those companies that make USB cables, not the resellers. The resellers usually don't like giving away who their suppliers are.