Normaly you can assign role to user by using transaction SU01, PFCG or SU10 or you also can do by using organization structure. Although in your compay not implement SAP ERP HCM but you can still use organization structure to assign role to user.
First you need to create organization structure using transaction PPOC, you can ask you friend in business departement because they understand well about organization structure. After you create the root organization structure, then you need to assign roles and user at the position level via PPOMW transaction.
After you assign User into position, then you need to perform user master data reconciliation using PFUD transaction. This transaction will check user should receive a role, You need to answer Yes, and then you can assign the role and the authorization profile in transaction SU01.
At last you can find organizational role assignment in transaction SU01 in Role Tab appear with blue text.