Yes, you can can recover Outlook email account if my phone number is changed.Contact Outlook phone number 1-888-617-0346 or 1-888-652-8714

I have moved to a different country and changed phone number. However, I didn't update this information on my email account. I didn't need to know my password to login in my Outlook email account because I used the Autenticator app instead. However, now I have a new phone and have lost access to the Autenticator app so now I am trapped because I can't access the Autenticator app as I don't know the password of my Outlook account. I also can't reset my password because the phone number is no longer in use (it was the phone number before I moved to the new country). I tried to find a contact support number to prove my identity and recover my account but couldn't find one. I also did complete the The recovery form is available at https://account.live.com/acsr but was informed that because I had the two-step authenticator my request was ignored. My question is very simple: Who and how should I contact to recover my Outlook email account? 
When it comes to account recovery/identity verification, the process is a bit rigid on purpose for security reasons and there's little anyone at support could do to help.

If you do not get code or no longer have access to your account security information (phone/email) to verify for a password change/recovery, unfortunately your only option is to fill out the account recovery form;
https://account.live.com/acsr

You will have to provide enough information to prove account ownership. see tip to help complete recovery;
https://support.microsoft.com/account-billing/b19c02d1-a782-dee6-93c3-dc8113b20c42

With the current account password, we have the option to update the security info (phone/email) to another with the remove info steps below, however the new info will be updated in 30days;

1. On the Security basics page https://account.microsoft.com/security , select the Update info button. If you're not already signed in to your Microsoft account, you'll be prompted to sign in.

2. You may be asked to enter a verification code to continue. If you don't have access to your alternate email or phone number, choose I don't have any of these and follow the instructions to replace your security info.

3. You'll see your security info under Security settings. Choose Remove for any you want to remove. You may be asked to add new security info before you can remove the old info.

https://support.microsoft.com/account-billing/bf2505ca-cae5-c5b4-77d1-69d3343a5452

To speak to someone from the Microsoft Accounts teams, use the chat link below and you can request a call back. 

https://support.microsoft.com/home/contact

1. Click on the link and in the search you could put in account issues
2. Scroll down and you should see the option contact support or sign in to contact support
3. you can sign in with a different email
4. for product select microsoft 365 and office and category select manage profile information
5. you should see the option Chat with a support agent in your web browser
6. confirm your email and it should take you to a support agent where you can provide your number and request a call back on continue via chat.