Personally, I would first check how the existing cord is wired. Those USB-C connectors aren't easy to measure, but if you have some fine tip probes it should be doable. Connect one end to one of the USB-A pins then probe the others and write down which pin or pins on the USB-C it connects to. Once you have all four pins and the shield mapped out, compare it to the standard pinout for a USB-C to USB-A cable as laid out here.
[image|3518468]
If you figure out what's different, you can either cut open an existing cord and rewire it as needed, or you can buy yourself a breakout board with solder points for each pin so you can wire the port up any way you need to. Something like this would do the job.
[link|https://www.digikey.com/en/products/detail/saiko-systems-ltd/BRK-USB-CPV3-0/15283090|BRK-USB-CPV3.0 Saiko Systems Ltd. - Prototyping, Fabrication Products - DigiKey]
Once you've got the cord figured out, be sure to come back and let us know what you discovered. Your investigation may well help the next person who comes along with the same problem.