The Father is the progenitor of every family on earth. The reference to “is named” implies that God is the authority of all these families of people. Paul presents God as both creator of all humanity, not just Jews, and the authority of all nationalities, not just the circumcised. Paul uses universal language to reflect the inclusive nature of faith in Jesus Christ. The point Paul insists upon is that God is the author of life through the Father, the strengthener and grantor of his great gifts through the Spirit, and the sealer of salvation for all mankind in the Christ/Son.
The Spirit draws on the fullness of God’s splendor. However splendorous God’s riches are is unknown and incomprehensible. And that is just the point. Paul prays for the Spirit to draw upon the riches of the Godhead to bring about strengthening and empowering of the believers. The Spirit functions in his usual overseeing manner by providing the equipping and strengthening believers need to interact with the Father. Paul prays for the Father to provide the agency of the Spirit so that believers experience and live by the indwelling power of God. They can know full communion with God through the empowering agency of the Spirit’s work.
The Son provides the “God with us” quality of God’s presence. The purpose for Paul prayer is that Gentile believers would experience the here and now presence of God in spite of what they have heard about circumcision as the agency of inclusion. Paul rebuts this idea and reveals the incredible truth that it is God through the strengthening of the Spirit for inhabiting by the Son that Gentiles experience Immanuel. The Trinity makes God’s indwelling in humanity possible. All the fullness of God dwelled in bodily form and now continues to dwell with the saved in faith.
There is no such thing as subordinated access. The Father lives in inapproachable light, so the Spirit strengthens the believer through sanctification to be able to house the Son. The Son mediates access to the Father through the Son.