Is it possible to assign a role to a user without a profile? If yes, how? (PFCG generate profile)
the profile for a role is generated when you activate ("generate") the authorizations you affected to the role using transaction pfcg (tab "authorizations", "button modify").
If you create a role without autorization, or without activating them, the role will not have any profile... You can however affect it to an user, using the standard su01 transaction.