I mean, there has to be some sort of system somewhere that helps the servers connect to each other. How does Lemmy.ca know that Lemmy.world exists? There must be some sort of authority that knows. There must be some sort of first step when a new instance appears that lets everyone know that the new server exists.

There literally isn't. New servers do not automatically federate with each other. Someone on the new server needs to manually start following users or groups on existing servers just to to establish any kind of connection. And even then, people on the existing server won't know that any users or groups exist on the new one.

It takes conscious effort by users to create connections and start content flowing between fediverse websites. There's no central authority of any kind. If someone doesn't make those connections, a fediverse website is functionally a stand-alone social media website.