FWIW I am unable to register a gmail for an account I deleted probably 8 years ago at this point. That said I don't know if there is anywhere where it explicitly outlines if it is or is not possible.
I pressed 'try another way' and they told me they don't have enough information to prove the account is mine.
Fuck off Google basically. They could at least be honest and state that a phone number is required, instead of pretending that it's for verification.
That is how I am locked out of a gmail account... eventhough I have the right username/password, and backup email, and typed in a phone number, Google won't let me back in.