I do not have access to the phone number to authenticate my Apple Account

While their online support article says for forgotten password, account recovery steps are also for a new phone number if you can’t sign in to update the number.  See "To see, add, or change your trusted phone numbers" at  Two-factor authentication for Apple Account - Apple Support and How to use account recovery when you can’t reset your Apple Account password - Apple Support

When going thru the account recovery steps  you need to first enter in that old number to show you know it. Then when you get to the step where it says it sent a code to that old number select the option most like “didn’t get code” and it will let you continue with your current number.

Always scroll down for additional options in small blue print if the  ones showing don’t apply to/work for you. 

When starting the account recovery steps the credit card is an extra option and not required. (See prior tip)

Account recovery is a two phase process once started. Phase 1 is the evaluation period, usually 24-72 hours but can be longer or shorter. This phase says Apple is evaluating your info and you’ll get an update after the posted time is over (people mistakenly think it means they’ll be able to reset the password immediately after this first phase.)

Once phase 1 is done it enters phase 2 where https://iforgot.apple.com/ will give you the final amount of days (can be weeks) you’ll wait. On that final day you’ll get a text/call, follow that text/call immediately. If you don’t receive the text or call, once the period specified in the original email is over, you can still go directly to apple.com/recover. Follow the instructions to regain access to your Apple Account.

If you can still sign into your account on another device you can investigate adding more ways to get a code such as multiple telephone numbers where you can receive a text or a phone call. The below is based on the section "About trusted phone numbers and trusted devices" in the article Two-factor authentication for Apple Account - Apple Support

To see, add, or change your trusted phone numbers use one of these methods:

● On your iPhone, iPad, or iPod touch: Go to Settings > your name > Sign-In & Security. Tap Two-Factor Authentication, tap Edit (above the list of trusted phone numbers), then enter your device passcode when prompted. Add or remove the number, then tap Done.

● On a Mac computer choose Apple menu  > System Settings (or System Preferences), then click your name (or Apple ID). Click Sign-In & Security, then add or remove a trusted phone number.

● Using a web browser:

1) Go to https://account.apple.com and sign in.

2) Follow Account Security options until you find one letting you change trusted numbers,

3) Click "+" to add a new number (you may be required to verify this number).

4) If you wish to remove an old number, click "-" next to the number.

Similar information for the iPhone can be found here --> Use two-factor authentication for your Apple Account on iPhone - Apple Support

If you had set up an Account Recovery Contact ( Set up an account recovery contact - Apple Support ) you can also get a code that way.

In a situation where a non-functioning device with cellular service was the only trusted number, transfer the cellular service to another device so you can receive a verification code on the other device instead.

If you can’t sign in, get access a trusted device, reset your password, or receive verification codes, you can request account recovery to regain access to your account. This article explains how to recover your Apple ID after a waiting period - How to use account recovery when you can’t reset your Apple Account password - Apple Support

You should consider making sure you have multiple trusted devices and telephone numbers (ask a friend or a relative).

You may also wish to read the articles 'Two-factor authentication for Apple ID' ( Two-factor authentication for Apple Account - Apple Support ) and 'Get a verification code and sign in with two-factor authentication' ( Get a verification code and sign in with two-factor authentication - Apple Support ). Various sections contain information that is useful in understanding about the trusted devices (an iPhone, iPad, or Mac that Apple knows is yours) system, and how to get a verification code on a trusted device or at a telephone number.