If they are serving all files, that should work for systems that check if you are the owner by asking to serve a file as a response to a challenge.

The copy is using ZeroSSL. This seems to use a similar mechanism like letsencrypt to verify certs. Maybe, you could get their certificate by serving the response to their challenge from your server. Not idea how to proceed from there.

Or activating the google webmaster tools. Maybe there's some setting "remove from index" or "upload sitemap" that could reduce its visibility on google.