I'm pretty sure you'll need an adapter that has a DAC built in. They cost a little bit more than regular USB C headphone adapters.
I had this same issue with a phone once, because the phone itself had no DAC (digital audio converter) built into the device, so the adapter needed to have a DAC for the phone to detect the headphones were connected.
If you post the phone model/headphones/adapter you're using, it would help to solve your issue.
