Google Indexing for Your Site
Groove sites are generally indexed by Google, automatically, within a few weeks from creation. You can check if your site has already been indexed by searching for your domain on Google. Specifically, go to Google and type site:example.com (and replace example.com with your domain name).
If you get any results, Google has already indexed your site. Google will continue to index any page that can get to by following links from your homepage.
If you get zero results, go to https://search.google.com/search-console/about and sign up with a google account to get your site indexed. They have a good set of instructions here: https://support.google.com/webmasters/answer/7474347?hl=en