'Naked' domains
By default, Google Sites have to be mapped to a subdomain and cannot be mapped to a naked domain.
A 'naked' (or 'bare' or 'root') domain is an internet domain name without the "www" or any other subdomains. For example, computerlanguage.com is a naked domain but www.computerlanguage.com is not, because it includes the www subdomain.
If you want your naked domain to point to your Google Site then you have to redirect the naked domain to your custom url
Google Workspace users - see https://support.google.com/a/answer/2518373
Personal account users....
If your domain provider lets you redirect your naked domain to the subdomain address (e.g. make example.com redirect to www.example.com) then you should configure that. E.g.
If you use Google Domains you can use its Synthetic records to get both your http:// and https:// top-level domain redirected as demonstrated in Steegle's video at 6:40.
Squarespace users - see https://support.squarespace.com/hc/en-us/articles/21222002826381-Connecting-your-Squarespace-domain-to-a-Google-Sites-site and
https://support.squarespace.com/hc/en-us/articles/206541837-Removing-the-www-from-your-domainGodaddy users - see https://www.godaddy.com/en-uk/help/forward-my-godaddy-domain-12123
(with this walkthrough by Kirkville web design PE Kyle - https://youtu.be/_aS1c1hRUe4?si=Z18xQgTXza_a7QWR&t=461 )
If you want both your http and your https top=level/naked domain to redirect to your www address then you can use NakedSSL free of charge for one domain. (no longer free)
Alternatively add an A record of @ (or your naked domain) that points to 174.129.25.170 (a free service from wwwizer.com)
There are other services, too. Such as https://redirect.name/ and https://redirect.pizza/ (free for up to 5 domains)