With Google Sites, you you can attach it to your domain like example.org.
In practice the
example.org
domain is not bound to Google Sites, but everywhere in this post, please substituteexample.org
with your own domain name.
In Google Sites, you can design web-sites and create “web address mapping” entries for it. However, you can only add a site mapping for a sub-domain.
But what if you want your www.example.org also to be visible as from example.org?
Then you get a nice error message “Required field must not be blank”: