Recover icloud account. Informations sent to icloud email. Infinite loop

I am trying to recover my mom's iCloud account that I have created a while ago.

Unfortunately, I do not remember the password to that account (neither she does). I have initiated the recovery process and it offers two options:

1) Send recover info to the email address

2) Answer secure question

There's an issue in both cases.

1) the email address the info is sent is the same email I am trying to recover access to (the icloud.com one)

2) The only secure question I am asked to answer is the "Birthday" which I believe I wasn't accurate when I set it in the first instance (certainly not my mom's ... I believe I was in a hurry when I set up the account by that time... I just wanned to quickly give her the iPad)

I understand that I have made some mistakes when I created the account: I should have be more careful with the data I was submitting then and I should have added additional email addresses to the account.

My question is if there is a way to sort this out... maybe use different ways to identify myself (via phone for example... I believe I wrote my number there and I would be able to receive an activation code if sent)...

Did you find yourself in similar situation?

Is there an email address I could write to in order to get help?

Otherwise, the iPad is in locked mode (i have set "Find my phone" to ON) until I log in with the correct details.