Wayne Grudem handles this in his Systematic Theology:
B. Adoption Follows Conversion and Is an Outcome of Saving Faith
We might initially think that we would become God’s children by regeneration, since the imagery of being “born again” in regeneration makes us think of children being born into a human family. But the New Testament never connects adoption with regeneration: indeed, the idea of adoption is opposite to the idea of being born into a family!
Rather, the New Testament connects adoption with saving faith, and says that in response to our trusting in Christ, God has adopted us into his family. Paul says, “In Christ Jesus you are all sons of God, through faith” (Gal. 3:23–26). And John writes, “But to all who received him, who believed in his name he gave power to become children of God” (John 1:12). These two verses make it clear that adoption follows conversion and is God’s response to our faith.
One objection to this might be brought from Paul’s statement, “Because you are sons God has sent the Spirit of his Son into our hearts, crying, “Abba! Father!”’ (Gal. 4:6). Someone might understand this verse to mean that first God adopted us as sons and second he gave us the Holy Spirit to bring regeneration to our hearts. But a few verses earlier Paul had said that we have become sons of God “through faith” (Gal. 3:26). Therefore Paul’s statement in Galatians 4:6 is best understood not to refer to the giving of the Holy Spirit in regeneration, but rather to an additional activity of the Holy Spirit in which he begins to bear witness with our spirit and to assure us that we are members of God’s family. This work of the Holy Spirit gives us assurance of our adoption, and it is in this sense that Paul says that, after we have become sons, God causes his Holy Spirit within our hearts to cry, “Abba! Father!” (cf. Rom 8:15–16).
Grudem, W. A. (1994). Systematic theology : An introduction to biblical doctrine (738). Leicester, England; Grand Rapids, Mich.: Inter-Varsity Press; Zondervan Pub. House.