According to Wikipaedia: Adoption is a process whereby a person assumes the parenting of another. Legal adoption permanently transfers all rights and responsibilities, along with filiation. In many jurisdictions, the adopted person’s original birth certificate is cancelled and replaced with a fabricated post-adoption birth certificate that states that the child was born to the adoptive parents. Ancient adoption practices put emphasis on the political and economic interests of the adoptor, providing a legal tool that strengthened political ties between wealthy families and created male heirs to manage estates. The use of adoption by the aristocracy is well documented: many of Rome’s emperors were adopted sons. Adrogation was a kind of Roman adoption in which the person adopted consented to be adopted by another.
Scripturally, adoption is purely a New Testament concept, and it behooves us to consider that those scriptures were written at the time of Roman domination and law. This then implies that ‘adoption’ as used by Paul is to be understood as being to authorise an adult heir to join a dynasty of power. When we read of ‘sons of God’ it tends to imply to us that we are merely infants, whereas under the Roman concept of adoption that Paul uses, the term ‘sons’ confers adult status and authority with power.
One of the aspects of Roman adoption included the above definition of having the birth records altered to reflect the new filiation. This even extended to a slave who would now be released from that bondage to then partake in the full rights of the adoptor (Romans 8:14-17a).
Infants, though born of the family, were not automatically given the title of ‘sons’, but were given an education that would encourage them to rise to positions of authority. Still it was only when they were officially adopted that their position as ‘sons’ was legally confirmed. Thus we read in Galatians 3:24 that the Law was given to be our tutor until we get to Chapter 4 verses 4-7 where we became true ‘sons’ of God. Even under common Jewish practices of the time, as we see in Galatians 4:1-3, children were not officially raised to a position of ‘sonship’ until the time appointed by the father. This time was often 30 years of age, though recognised as (trainee) adults at 12 or 13 years old. (Note: Jesus commenced His ministry at age 30 after His baptism when God says, “This is my beloved son”.)
It’s interesting to note that in Ephesians 1:5 we read, “ having predestined us to adoption as sons by Jesus Christ to Himself, according to the good pleasure of His will”, which plainly states that this is not a spur of the moment, hands up confession of the one being adopted, but rather the eternal plan of a loving Father, even since before the foundation of the world! This great event entitles us to all that the Father has, including every blessing (Eph 1:3), and that we are now co-heirs of His Kingdom, ruling and reigning with power and authority.
PS: All of this applies equally to daughters.