How do I actually start account recovery process?

See the following Apple articles:

Set up an account recovery contact

Set up an account recovery contact - Apple Support

How to use account recovery when you can’t reset your Apple ID password

How to use account recovery when you can’t reset your Apple ID password - Apple Support

Scroll to -> What is account recovery?

Account recovery is a process designed to get you back into your Apple ID account when you don’t have enough information to reset your password. For security reasons, it might take several days or longer before you can use your account again. We know this delay is inconvenient, but it's important so that we can keep your account and information safe.

Account recovery might take a few days or longer, depending on the specific account information you can provide to verify your identity.

Hi kayson115,

You too may find an reply to look for the answer in How to use account recovery when you can’t reset your Apple ID password - Apple Support is kind of a non-starter since it doesn't actually tell you how to start it. Nor do the dozens of web sites claiming to tell you since they all pretty much tell you to set up a recovery contact first. Not everybody does that otherwise you basically don't really need to do the true account recovery.

I have never needed to use account recovery myself, and I am sure you'll understand if I don't want to mess with my account trying to find out how it works. From what I can tell, if you go to https://iforgot.apple.com/ and try to reset your password and cannot use the standard ways of account verification (trusted numbers or devices) you should eventually get some option to let you start the account recovery process.