Cloud Run hosted API and Firebase App hosting communication using VPC connectors

Hey guys,

I have a Node JS API hosted on Cloud Run and next JS hosted on firebase app hosting. Is it possible that only my Next JS app can access my API, public access disabled. Seems to be possible using VPC connectors. But not sure if its doable for Firebase app hosting, couldn’t find any document. I cant use service-to-service communication, because some endpoints are public and passing token in Authorization header for public endpoint doesn’t feel right

Appreciate quick help
Thanks