To find a matching connector you’d normally measure the distance between the pins, at least within the same family of connectors. In this case there are so many similar yet subtly different connectors though, I’m not sure you’ll find the correct one. At any rate, soldering would probably be easiest (even if it’s just aoldering the wires together).
There may be another approach though. With this type of connector, the pins are normally crimped onto the wire and then stuck inside the plastic case. You could buy a few connectors that look like they might fit, remove the pins (use a small tool such as a 0.5mm screwdriver) and try inserting the pins into the case of the original connector in the correct order.
Edit: the thick black wire (original) and the grey one (USB-C connector) should be the same.