Google Analytics

If you want your site to appear in search results make sure you have not selected  Request public search engines to not display my site 

You can request how public search engines treat your site.

Note: This option is only available if "Anyone on the web" can view your site.

Use Analytics with your site

You must create a UA (Universal Analytics) code. See this page for information.

VERIFICATION: If you have not managed to verify your Site using the verification method recommended by the Google support article use this one instead:,This article uses a different method which is easier. 

New Google Sites - Add to Google Search Console

See also this update

Once you get your site added/verified in the Search Console, you can Ask Google to Recrawl Your Site using the "Use the URL Inspection tool" option.  Do not use the sitemap option since New Sites do not use sitemaps.

Note that Google Search Console has temporarily disabled index requests at the moment there's no way to actually get your new Google Site indexed