Hello,
Unfortunately, you cannot close your Microsoft account without verifying your identity through one of the security contact methods on the account.
Microsoft recommends that account holders keep at least three verification methods active. That way, if one becomes outdated or stops working, you may still be able to use another to sign in.
When you change your password, Microsoft may ask you to verify that you own the account using the recovery phone number or email address associated with it. If your landline cannot receive verification codes, select “I don’t have any of these” on the Verify your identity screen and follow the prompts.
Note:
If you remove all your existing security information and replace it with new information, your account will be restricted for 30 days. Microsoft cannot shorten this waiting period.
In the meantime, you can remove any payment methods linked to your account to help prevent unauthorized charges, move your files to a local drive, and export your emails. After the 30-day period, once your security information has been updated, you can reset your password and enable two-step verification for added security.
How to help keep your Microsoft account secure
Let me know if you still need more help.