There is no alternative to the listed pairing procedure. That is the way.
➔ You should use the key combination of both Menu and Volume Up.
If asked to bring it closer, the ultimate closeness is to lay it on top of the Apple TV box.
Verify that you have a Siri Remote. Identify your Apple TV remote - Apple Support. The first listed connect procedure is only for those remotes.
For the new Siri Remote (2nd generation), verify that the system software is up-to-date (tvOS 14.6 at this time).
Verify that the remote’s battery has been charged.
Verify that other devices do not interfere (e.g. lay your phone away at some distance, instead of on your person).
Verify that the remote isn’t broken. Drop it too many times, and it will stop working at some point. Fluid damage may seem okay when dried up, but is more destructive over time (oxidation).
If you did as described and you still need help, you may contact Apple Support.
If needed, you can buy a replacement remote.