What does the `lsusb` command say about it?
If the output line for the dock includes `ID 17e9:600a`, then it is this one: a DisplayLink dock.
DisplayLink docks essentially provide an extra USB-connected almost-GPU that needs its own `evdi` driver module. The driver package also includes firmware that is needed for the USB-GPU to work, a `libevdi` library, and a closed-source DisplayLink Manager application.
You could get the firmware and the application by extracting the driver package and then build the driver and library from sources available on GitHub.
The ArchWiki also seems to have advice on using DisplayLink devices on Arch. As far as I've understood, the procedure should be essentially the same as with the USB-3.0 DisplayLink devices, although your dock uses the newer USB-C connection.