The Get Started button and the Persistent Menu is not showing if the user registered for Messenger with a phone number, without a Facebook account. I know that I can't get profile information (error code 2018218), but from the documentation I have not found anything about the properties get_started and persistent_menu of the Messenger Profile API. Has anyone encountered such a situation?
I finally found a solution. From the Facebook developer console, go to your app Settings -> Advanced, in the App Restrictions section set "References Alcohol" to NO and "Age Restriction" to Anyone(+13).