Using a DNS server, somewhere. Unless you manually gather the required IP addresses of whatever services you want and build up a hosts file, like how the original ARPANET worked.

The requests will come from somewhere and go somewhere. There is not magic “you don’t see me” domain resolution system. Even DoH or DoT, you have to trust the resolving server isn’t going to track you.
Whether that request is to a DNS server you run on an IP linked to you, or from the gateway of your VPN to a DNS server to do not run… It’s always going to come back to an IP address of a VPS that is linked to you.

I don’t get what you are trying to do, you haven’t explained it well, and your being hostile as fuck all over the thread.

If you really want anonymity, use TOR?
Other than whatever-the-CIA/NSA/MI5/MI6/5-eyes is doing with timing attacks and their own relay/exit nodes, that’s about as anonymous as you can get