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

How to create a Google site and use it with a Google domain?

I registered a domain via Google Domains (let's call it exemple.com). I then created a Google site (let's call it sites.google.com/site/example123)

Now, I'm trying to point exemple.com at this address.

To that end, I added a CNAME record on Google Domains, but as I understand it, I also need to configure the Web address on Google Sites.

However, when I enter www.example.com or exemple.com there, it tells me

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

Without further explanation or trick. Googling was not very helpful – I found forum posts 7 years ago complaining about this.