Theos is a concept. The concept expresses Deity. We understand Deity to be divine nature. That divine nature is, for example, eternal. An attribute of Deity, of divine nature, is the fact that Deity, divine nature, is eternal.
This divine nature is a feature, so the New testament scriptures make clear, of the Father. And also of the Son. And also of the Holy Spirit. The Spirit is called 'the eternal Spirit', Hebrews 9:14. The one who was manifested to the apostles (whom we know to be Jesus Christ, who is called 'the only begotten Son', John 3:16) is described as 'the life, the eternal, which was with the father', 1 John 1:2. If that life eternal was with the father, then he who begat that eternal life is also eternal.
Thus eternal life is a feature of Father, Son and Holy Spirit. And so are other attributes of Deity so of the Father and of the Son and of the Holy Spirit.
Fatherhood is an attribute of Deity. Sonship is an attribute of Deity. Spirit is an attribute of Deity.
Jesus said, 'I and my Father are one'.
A perfection of divine unity, in one Holy Spirit.
So when one states the concept Theos, or Deity, one is expressing such attributes, collectively. But one may wish to emphasise the divine-ness of the Father. And if so, one may say 'God Father', emphasising the divine nature of the Person of the Father.
And we know, from studies regarding Sharp's rule, that such references are also made regarding Jesus Christ :
... the glory of our great God and Saviour Jesus Christ, [Titus 2;13 Young's Literal Translation]
In respect of Ephesians 4:4-6 :
There is one body, and one Spirit, even as ye are called in one hope of your calling; 5 One Lord, one faith, one baptism, 6 One God and Father of all, who is above all, and through all, and in you all. [KJV],
I would say that reference is made to each divine person in turn.
Firstly, as is sometimes the case in scripture, the Spirit.
Secondly, the Lord, meaning (in this place) the Lord Jesus Christ.
Thirdly, the God and Father of all, wherein I would see an emphasis and a reference to the fact that the Father is God of the Lord Jesus Christ, in respect of his humanity. And thus, those of whom God is the Father by a new birth are brethren of Jesus Christ sharing the same origin of life (spiritual life, new life).
Even the Father addresses the Son (in his deity) saying 'Thy throne, O God ...' Hebrews 1:8 KJV.
So the Father may be seen as the God of the Lord Jesus Christ in regard to the Deity of the Son of God, in his begetting. Yet the Father calls the Son 'God' in respect of divine being.
And the Father is the God of the Lord Jesus Christ in regard to the human nature of the Lord Jesus, also.
But in this place, I see the emphasis to be that the person of the Father is God of all.
I would therefore, myself, see this place as meaning 'God and Father of all' that is to say of all those chosen in Christ, sanctified by the Spirit and in union with Jesus Christ through the begetting of the Father. And also, God and Father of Lord Jesus Christ who is equal in deity, but subject in humanity.