Azure may not permit direct access as root, but that is still what you need to use to access WHM on the server. There's no way around that.
I'm not sure how well the installer would work run under another user, so that system may not work properly.
Once you are logged into SSH, I would expect you to be able to run "sudo su -" to gain root access. Once you have accessed root, you can change that user's password to something you know. If that isn't working how you expect, you'll need to contact Azure directly to see how you can access root over SSH for your particular type of system.