How do I change/recover the Apple ID password if I don't know the phone number that was used?

See if you can get an email option.

Enter the Apple (iCloud) ID and click Forgot Password.

Apple ID - Manage            

Apple ID – Forgot Password    

If necessary, contact Apple ID Support. See the Apple Support articles below for contact information.  

Apple ID - Official Apple Support.    

Contact Apple for help with Apple ID account security - Apple Support.   (Link doesn’t always load)  

Get Support          Work through the screens to get a chat option. 

Apple Support schedule phone call

https://twitter.com/AppleSupport

From the Apple Support article below. 

Without proof of your identity via security questions and other carefully selected criteria, Apple Support can't help you reset a password or perform any other actions on your account. These policies are audited and reviewed on a regular basis.

Security and your Apple ID - Apple Support.      

See If you forgot the passcode for your iPhone, iPad, or iPod touch, or your device is disabled  https://support.apple.com/en-us/HT204306, especially the section entitled Remove your passcode. 

Remove your passcode says if you don't have a computer to use, then "borrow one from a friend, or go to an Apple Retail Store or Apple Authorized Service Provider." Of course the last option usually is not available now.

Later the document says: "If you can't update or restore your device using recovery mode, or you can't use recovery mode because of broken or stuck buttons, contact Apple Support. Then follow the steps to set up service for your iPhone, iPad, or iPod touch." 

You can contact the cellular service provider , with your personal details like first and last name , proof of identity , they keep the records the number can be obtained from them / in case if you shared the number with friends .

The mobile number is your actual Apple ID address see the article https://support.apple.com/en-us/HT207944