How to connect a custom domain to a cloud function express.js render

I’ve created a cloud function that renders dynamic web pages using express.js, handlebars, firestore, and vue.

Using rewrites I can point the main domain to these dynamically generated pages, like: ‘mydomain.com/firestoreID’.

But i’m looking for a way to have customers (who have generated their own website) connect their own domain. So that: instead of only giving them a ‘mydomain.com/theirbusiness’

Giving them their OWN ‘domain.com’ Pointing to the cloud function, generating their unique website.

Hope someone can help me out here. Can’t seem to find anything about this..