Proper way to connect signals to USB Type-C receptacle
You will want to refer to the USB Type-C Specification. (The USB Implementers Forum has these and other documents.)

One of the main features of the Type-C connector is that it can be flipped. I think section 4.5.1.1 of the linked document may be of most interest to you:


  Since the USB Type-C plug can be inserted in either right-side-up or upside-down position, the hosts and devices that support USB data bus functionality must operate on the signal pins that are actually connected end-to-end. In the case of USB 2.0, this is done by shorting together the two D+ signal pins and the two D− signal pins in the host and device
  receptacles. In the case of USB 3.2 SuperSpeed USB or USB4 TX/RX signals in a single-lane
  implementation, it requires the functional equivalent of a switch in both the host and device to appropriately route the TX and RX signal pairs to the connected path through the cable. For a USB 3.2 SuperSpeed USB or USB4 dual-lane implementation, the host and/or device resolves the lane ordering.


I'm not quite sure how your project fits into the various examples given, but I think that you'll likely find what you're looking for there.