It is the Account Recovery link that needs to be used. What happens when you try to start Account Recovery? Don't forget to read the section for what may cancel the Account Recovery request.
As for manual verification, there is nothing provided when creating an Apple Account that proves positive identification for ownership of the account that can be verified. That is the purpose of the Password, Trusted Device, and Trusted Phone number and Account Recovery may be possible without those, but that is done using the link and possibly requiring a waiting period if not enough information is available. Contacting Apple will not speed up that process or give you immediate access to an account bypassing those automated steps for a standardized approach for verification.