We reconcile the fact that Christians are said to be both begotten/born again and adopted by acknowledging the different natures of the "begetting" with regards to being born again and adopted.
Born again refers to the beginning of spiritual life. See John 3:1-14. Our flesh is begotten of Adam, the flesh, and man. Since flesh and blood can not inherit the Kingdom of God (1 Corinthians 15:50), we require a second birth, a spiritual one, in order to enter into the Kingdom of God. In Christ, we are not born of the flesh, but born in the Spirit (see John 3:1-14). "In Christ" means because of our full inclusion in his body, even before we were born.
Adopted refers to our legal standing of relationship with God. God decided in advance to adopt us into his own family by bringing us to himself through Jesus Christ. This is what he wanted to do, and it gave him great pleasure (Ephesians 1:5). This legally binding adoption is multifaceted and dictates our inheritance, our authority, and our relationship with the Father in his Kingdom.
We are sons of God as a result of our adoption, which is simultaneous but not synonymous with our second birth.
No one can say "I am begotten of God" unless he can already say "I have been born again," because if he has not been born again, then he is begotten of Adam, even of the devil (John 8:44), but he is not begotten of the Father, because that born of the flesh is flesh and that born of the Spirit is spirit (John 3:6). We were included in Christ when we heard the message of truth, the gospel of our salvation. When we believed, we were marked in him with a seal, the promised Holy Spirit. (Ephesians 1:13). So, spiritual birth and adoption to sonship are distinct but simultaneous immediate consequences of converting faith.
Now, let us look at the structure of the Greek from John 1:12-13 (verse 13 is missing in the Greek text in the question):
ὅσοι δὲ ἔλαβον αὐτόν ἔδωκεν αὐτοῖς ἐξουσίαν
but as many as received him he gave to them authority
τέκνα θεοῦ γενέσθαι
children of God to become
τοῖς πιστεύουσιν εἰς τὸ ὄνομα αὐτοῦ
to those trusting on the name of him
οἳ οὐκ ἐξ αἱμάτων οὐδὲ ἐκ θελήματος σαρκὸς
the ones who not from blood nor from will of flesh
οὐδὲ ἐκ θελήματος ἀνδρὸς ἀλλ᾽ ἐκ θεοῦ ἐγεννήθησαν
nor from will of man but from God were begotten
The sentence structure of the Greek Scriptures tend to be very repetitive, especially John’s Narration in the first chapter. Recall how repetitive the clauses are at the opening (this is a word-for-word):
“In the beginning was the logos and the logos was with God and God was the logos this one was in the beginning with God all through him existed and apart from him existed not even one which exists.”
There are two similarly repetitive phrases in John1:12-13, each starting with a (logical- not grammatical) conditional clause. They are related by “he gave them authority to become,” (denoted below by --> ). Though it’s only written in the first phrase, and implied in the second. This is common. The similar phrases are:
- To those who received him --> children of God
- To those trusting on the name of him --> the ones not from blood … but from God were begotten
That is, "to the ones who received him who trust in his name he gives the authority to become children of God who not from blood nor will of flesh nor will of man but from God were born "
The notion of sonship (or being sons of God, or being of God) always refers to this adopted status through Christ for the righteous in him, indeed:
But the one indeed of the slave woman according to the flesh is begotten, but the one of the free woman through the promise.
ἀλλ’ ὁ μὲν ἐκ τῆς παιδίσκης κατὰ σάρκα γεγέννηται, ὁ δὲ ἐκ τῆς ἐλευθέρας διὰ τὴς ἐπαγγελίας.
Those who are brought in through the promise were originally sons of Adam (here Hagar), from whom we inherited our flesh. The promised Christ has made it possible for us to inherit our glory- the right to be called the sons of God. Ordinarily, if a father were to adopt so many sons, the inheritance of the principle among them would decrease every time. But in our Father's house there are many rooms, and our inheritance is the principle among the sons, Jesus the Messiah (Rev 21).