Is there a way for users to visit our site using a custom domain without the search engines show the contents with the link?

Issue

The following article suggests that we cannot remove the default domains: https://help.liferay.com/hc/en-us/articles/21806552291981-Is-it-possible-to-remove-the-default-domains-lfr-cloud-in-Liferay-PaaS, but we do not want the search engines to show their contents with the link to *.lfr.cloud URL. So is it possible to remove the default domains *.lfr.cloud in Liferay PaaS? Or just for users to visit our site using the custom domain accordingly?

This feature is currently under development internally with an expected ETA of next year 2025 (official date TBD). The specifics are not yet concrete, but in short customers will be able configure CDN and WAF settings more autonomously in the future.
Now as for options you can implement currently to manage search engine indexing and user access that may help we'd recommend:

Blocking Search Engines: Configure robots.txt to disallow indexing of *.lfr.cloud URLs. You can add this configuration in the webserver service settings to guide search engines to avoid indexing these URLs.
Redirect Users to Custom Domain: You can configure redirects in the nginx.conf file to direct users accessing the *.lfr.cloud URLs to the custom domain. This customization does require managing updates in your nginx.conf file after each platform release, as configurations may reset.
Workarounds:
- nginx.conf Customization: As mentioned, you can add rules to your nginx.conf to redirect all traffic from the *.lfr.cloud domain to the custom domain.
- Custom DNS and SEO Configurations: While the default domain remains as a backup, use SEO settings to prioritize the custom domain and reduce the visibility of the default one in search results.