I bought a thing with 4 USB 3 ports, that is mounted in one of the PCI card slot openings at the back of the case. It is just the four USB ports mounted on a piece of shaped metal… plus with four cables coming out of it; at the other end are 2 plugs for the USB header socket on the motherboard (2 ports per header). (Mine is USB 3.0; I am not vouching for whatever is most recent.)
It took me a while to work out what to search for. I think “USB header adapter adaptor” is right/best; add “mainboard” if it helps. The big difficulty was finding one with 4 USB ports, as opposed to 2. [Later: perhaps start with “ mainboard usb header adapter adaptor "4 port" ”.] It was mildly more expensive than I expected, but nothing untoward.
(Of course, you can compromise and use 2 of {2-port ones}. …Or just use 1 of 2-port one, and do without the other two USB ports.)
With this, you can buy pretty much any case you want, and have all 4 (or whatever the motherboard supports) USB sockets available. The (only) downside is the obvious one, that the ports are at the back. For the price difference, I think it is worth it . (I always position my cases with the opening side forwards, so that the front, back and internals are all somewhat accessible.)
The link to the product I bought is obsolete.
Here is what it looks like, conceptually.
eSATA & 2xUSB 2.0 Back Plate for Mainboard
Here is a 2-port one (otherwise) like I got.
USB 3.0 Back Plate for Mainboard 2 port
Here are some 2-port alternatives.
https://www.techbuy.com.au/p/174074/USB_ADAPTORS_CONVERTERS/BitFenix/BFA-U3-KU3IU3-RP.asp
Interested in using the USB Thumb drive as an internal storge device in your Desktop? This Embedded USB type-A adapter may just be the solution y ...
www.techbuy.com.au
https://www.mwave.com.au/product/startech-2-port-usb-motherboard-header-adapter-ab64806
I hope this helps!
Edit_01.
You can also get ones that come out the front, in a drive bay. For that matter, you can get a front drive bay accessory with about 6 USB ports, an SD card reader, audio sockets and… everything.
p.s. What I got is not exactly what the OP wants, but I am sure they can translate the concept. If they wants just 1 USB C port (as opposed to all 4 supported), it should be pretty easy to find something… although conversely my offhand searches are not finding anything higher/other than USB 3.0.
Edit_02.
See perhaps…
https://www.amazon.ca/EZDIY-FAB-Internal-19-Pin-Header-Adapter/dp/B082X5HT94
(You could then use an extension cable.)