cname – How do I create a Google site and use it with a Google domain?

How can I create a Google site and use it with a Google domain?

I have registered a domain through Google Domains (let's call it) example.com). I then created a google site (we call it sites.google.com/site/example123)

Now I try to show example.com to this address.

To do this, I've added a CNAME listing in Google Domains, but if I understand it, I'll have to configure that as well Website URL on Google Sites.

But when I enter www.example.com or example.com there it tells me

This location is already in use by another service. Please select another one.

Without further explanation or instructions. Googling was not much help – I found some forum news from 7 years ago that complained about it.