If they schedule a call indeed, you should get an email - this email has the case number in it.
If you never got the email, that might explain why you never got the case number either.
I opened a live chat on their site and talked to someone who offered for an engineer to call back (not that it went as planned, the wrong guy contacted me etc, but that's another story).. but she confirmed my apple id is what i can receive emails on.. and i got one with the case number and the phone they would call.
When it happens you get a call that says 'thank you for calling apple, press 1 for an advisor' who then talks to you
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Try searching your mail for "apple + case" and see what comes up, maybe you overlooked the email?
on
https://getsupport.apple.com/ you can enter the repair or case id.
If the page doesn't load with one, then at the bottom it should have view your devices or view your cases/repairs (which brings you to the input field for the case id)
If you simply didn't get one, contact them perhaps and tell them you were supposed to get a call but never did and didn't get an email with a case id either .. if they can look into it. You provide your apple ID and they can confirm who you are and tell you.