No, they are not “roles” at all.
A role is something a person does temporarily for a specific purpose, and put off or set aside when the purpose is achieved. An identity is something a person is and cannot be set aside.
God the Father is always God the Father. He doesn’t put that aside. God the Son is always God the Son.
Not sure why you balk at referring to Father and Son as eternal roles, because the Bible does, so please explain.
Role = relationship = person.
The OT Shema (Deut. 6:4) teaches that God is one, and the NT also affirms that there is one God (Eph. 4:6, 1Tim. 2:5). However, the NT teaches that God relates to believers in three ways simultaneously: as the Father, as the Son and as the Holy Spirit (1 x 1 x 1=1).
The Father/Parenthood of God is indicated in Jesus’ model prayer (Matt. 6:9), throughout the Gospel of John (John 3:35, 5:17-18, etc.), and in the epistles of Paul (Rom. 4:11, 8:15, Phil. 2:11). God the Father and
Christ’s Sonship are discussed in Heb. 1:1-4. The Son of God also is mentioned by John (John 1:14, 3:16, etc.) and by Paul (Rom. 1:4, Gal. 2:20, 1Thes. 1:10). The
Holy Spirit is mentioned in three successive chapters in John (John 14:26, 15:26, 16:13), frequently in the book of Acts (Acts 1:5, 2:4, 9:17, 13:2, 19:2), and in many of Paul’s letters (Rom. 8:4-26, 1Cor. 6:19, Eph. 4:30) as well as in some of the other epistles (2Pet. 1:21, Jude 20).
Apparently, Christians failed to explain to
Mohammed (c. 610) how God is able to relate to Himself and to creation as a Triunity, and so the prophet’s teaching stressed that there is one God and implied that the Christian gospel is false. It might have been helpful for him and others who stumble at NT doctrines to discern which aspect of the triune God is the subject of various biblical statements. These divine aspects or “persons” may be distinguished by role: God the Father as creator or initiator (Gen. 1:1), God the Son as Messiah or mediator (1Tim. 2:5), and God the Spirit as indweller (Rom. 5:5). For example, 1John 4:7 says love comes from (is initiated by) God (the Father), Gal. 5:22 says that love is a fruit of the (indwelling) Spirit, and Eph. 3:18 speaks of the (mediating) love of Christ (Rom. 5:8, Eph. 2:18).
We can denote these distinctions by the use of three prepositions: God the Father is over all creation (Eph. 4:6), God the Son is Immanuel or with humanity (Matt. 1:23), and the Holy Spirit is within all believers (Eph. 1:13). A single passage that comes closest to indicating this distinction is Eph. 3:14-19, in which Paul prays to the Father that through His Spirit of love Christ would dwell in believers’ hearts (also see 1Cor. 8:6).