New Google Sites in Google Search results

The question applies to only Google Sites New (version) as it currently doesn't support web URL mapping. More info here under section Web address mapping :

https://support.google.com/a/answer/7198710?hl=en&ref_topic=6399171

So I made my site publicly available and can access it via the sites URL. I then did a 302 URL forwarding in my domain DNS so if I type in the domain.com it gets redirected to sites URL -- All good so far.

My question is how come some users are managed to have their URL showing up in Google results. Example Query in Google :

https://www.google.com.au/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#newwindow=1&q=Made+with+the+new+Google+Sites%2C+an+effortless+way+to+create+beautiful+sites.

you will see some sites for example

These sites - ArchSci2020 and Mr. Arnote's new google Site have their URL displayed and Title doesn't contain the word Google Sites. Example if you try the following query where I am looking for the footer phrase

https://www.google.com.au/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#newwindow=1&q=%22Made+with+the+new+Google+Sites%2C+an+effortless+way+to+create+beautiful+sites%22

I am using Google Domains and it only allow URL forwarding -- what are they doing differently?

Thanks.

I think they are indexed by Google with their real domain name because they use iframes or invisibles redirects configured in their registrar panels like Namecheap (for mrarnote.com for example).

According to Namecheap support:

Recently, Google has released a NEW version of Google Sites (it can be accessed through https://sites.google.com/new), however, it has no option to use a custom domain with it. If you still would like to use this version of sites with your domain, you may set up the connection via URL forwarding (more detailed instruction on how to set up the URL forwarding can be found in this article)