Unfortunately, have not been able to check or confirm this myself, so not sure, but found some articles below if you have any interest.
First make sure your Type-C display output is connected to the Nvidia graphics if possible, by connecting an external monitor and confirming it shows up under the Nvidia control panel settings rather than Intel graphics settings which is not what you want to see for VR. It's not clear on my end, but you might also check under device manager and display adapters to check if your unit includes both Intel and Nvidia display adapters or only Nvidia.
According to the Oculus site below, doesn't sound like they are supporting type-C connections or type-C adapter for the Oculus Rift S officially, but that doesn't always mean it will not work.
USB Type-C Connection with third party adapter: Currently, we cannot make any recommendations for USB-C -> DP. If this changes, we'll update this article to include any supported adapters. "
If you check the Oculus forums page below and trust it, sounds like a GX701 customer has been able to get a type-C to display port adapter to work with their Rift S.https://forums.oculusvr.com/community/discussion/75126/will-the-new-oculus-rift-s-function-properly-...
More discussion about the topic at the third-party site below if you want to take a look, but don't know if everything is correct or not.https://uploadvr.com/oculus-rift-s-valve-index-no-hdmi/