I thought we were all a child of God… nope.  (Romans 3:10-12, 23, Romans 5:12,  John 8:44, 1 John 3:8-10, Romans 8:9, Ephesians 2:12)

Is God my Father… spiritually speaking… not until you're born again. (John 1:12-13, John 3:5-7, Romans 8:15-17, Galatian 3:26-29)

We were apart from God… separated.  We were brought back into right fellowship by the spiritual rebirth.  This rebirth is what gives us access to what we by nature were cut off from… similar to the process of adoption.  An adopted child is brought into a family and is accepted as and has the same rights/privilege as the natural.  By being born again, we receive his Spirit, and are now his children (Romans 8:15-17).  

We have an obligation as God's children... (2Tim. 2:19, 2Cor. 5:17, 1 John 3:2-3, Romans 8:12-14, Galatians 5:16-25, Ephesians 4:1-3)

Greco Roman Adoption Process – to identify an heir (Usually Adults not Children)

• Critical Aspects: Legal appointment as a son by declaration, the promise of an inheritance, and a condition against rebellion.
• Adoption would result in an adoption of power for the adopted child as the status of the adopting family was immediately transferred to the child.
• The actual adoption was often operated like a business contract between the two families. The adopted child took the family name as his own.  Kept his GIVEN name but took on the new family’s CLAN and FAMILY name.
• An adopted child received a new identity. Any prior commitments, responsibilities and debts were erased. New rights and responsibilities were taken on just as though he were a natural born son.
• In ancient Rome, the concept of inheritance was part of life, not something that began at death. Being adopted made someone an heir to their father, joint-sharers in all his possessions and fully united to him.
• In the Roman system, the man or boy being adopted was alieni iuris (still under the control of a pater familias, the patriarch or head of a family). The son who is not his own master (alieni iuris) switched from the control of his own pater familias to the control of his adoptive pater familias. This process was called adoption.  He had to leave everything from his past life behind… he owned nothing and could bring nothing… just himself. 
• Under Roman law, a free non-citizen (peregrine) could not be adopted by a citizen. A slave could be freed to become a Roman citizen; the freedman, who was now a Roman citizen, could then be adopted.
• Was expected to respect and honor new parents as though they were his real parents.
• At any time the adoptee could be emancipated by his adopted father.  Emancipation is the termination of parental control and revokes all the rights that one possessed by having been a part of the family.  All property and inheritance rights would be completely lost.

Sources

Adoption in ancient Rome - Wikipedia

How the Roman practice of adoption sheds light on what St. Paul was talking about (aleteia.org)

Biblical Adoption Is Not What You Think It Is | Christianity Today

Adoption in the Roman Empire - Life in the Roman Empire (carolashby.com)

Adoption in New Testament Times (liberty.edu)