Self- assessment registration date security question

I have a new phone number so I am unable to receive the code to login. I have tried to reset this with customer services over the phone (there is no option to do this online for me) and the last security question they asked was "when did I register for self assessment?" I explained I could not answer and they said they can go no further. A letter was received about registration at the time, but this was 8-9 years ago, I do not have it and I have no idea what exact date would be. It could be anywhere from April to October during that tax year. How can I find out my registration date or gain access to my account another way please?

Hi

If you'd like to update your contact number but are unable to confirm the security information requested, please write to us at
Pay As You Earn,
HMRC,
BX9 1AS
confirming you name, address, date of birth, National Insurance Number and new contact number, and confirm that you'd like to update this contact number.
We will then contact you if any additional information is required.

Thank you