Mapping to Domain
Your site must be published to a sites.google.com URL before it can be mapped to a domain.
You can use a custom domain for a site published on new Google Sites.
Enter a site name in the 'Web address' box. Use only lowercase letters, numbers and dashes. Your site URL will appear below the box.
If you want to use a custom domain that you own click Manage.
Alternately you can just publish the site and set up the custom domain later.
Note: This website is now mapped to: https://new.k8oms.net and https://www.k8oms.net/ and https://www.k8oms.page
If you want a domain link that goes to a particular page in your site, use forwarding instead of mapping. For instance rate.k8oms.net
I did this by setting up forwarding in my domain panel to forward the subdomain 'rate' to a page in the site. See the image below to see how I did it in Godaddy.
New Google sites are automatically secure (https) at the native Google URL and at the mapped domain, so it is not necessary to purchase a SSL certificate. If necessary, use this procedure to refresh the certificate: Remove the custom URL from your site, wait about 15 minutes then add the custom URL again and that will generate a new SSL certificate.
I don't see custom domains option
There are 2 reasons that you cannot see the custom domain option in Google Sites: