The site you build with Site Editor can always be accessed from the free Site Editor’s domain and will never expire. You can configure the free Site Editor’s domain from SETTINGS > Domains in Site Editor. Read Using Site Editor’s Domains to learn how.
You can also hide the Site Editor’s domain from your visitors by connecting a domain you own from a third-party domain provider to your Site Editor’s site and setting this connected third-party domain as primary.
If your built-in domain is still displayed after making a connected third-party domain primary, you can ask Google to update your site by submitting it to Google Search Console for re-indexing. The same principle applies to other search engines which you can also contact with the request to re-index your site.