Being a son of God is one of the grand privileges and honors that God freely gives to those who have put their trust in the redemptive work of our Lord and Saviour Jesus Christ (Romans 3:21–26). However, it is not something that is unique to those who have believed in Christ in this present dispensation of God's grace. In fact, it is the kind of relationship that God originally wanted to have with Adam and Eve in the garden. A relationship of intimacy, connection, God being a Father to man in creating them, caring for them , providing their need for growth and development, and educating them to become like Him. This education was begun in the garden, and we see evidence that Adam we becoming like God in his thinking, his behavior, and his labor. However, that was interrupted by the deception Eve suffered and the choice Adam made to gain the "knowledge of good and evil" another way. By doing so, they rejected the relationship God offered them of being a son and daughter.
In working out a plan of reconciliation, God created a nation of his own and separated them from the rebellious nations of the earth. Israel was also going to be adopted and treated by God as a son (Exodus 4:22–23). However, soon after coming out of Egypt, they rejected the provision of the LORD and His Fatherly role, and chose instead to be dealt with by God on the basis of their own works.
God did not give up, however. God anticipated this, knowing He would have to make man (Israel included) capable of again having that sonship kind of relationship with Him. To do so, He must first take care of man's sin. So, he promised Israel to send His own son into the world, the Lord Jesus Christ. Christ came and was the perfect son. Then, in laboring with his Father, He gave his life on the cross to satisfy God's wrath against sin, and to destroy the effects of sin in man. This gave Israel the opportunity to become reconciled to God and become sons of God just as John 1:12–13 states.
God then revealed a mystery through the apostle Paul, and extended this privilege to the Gentiles as well. Today, anyone who believes the gospel of God's grace is given the privilege of being God's son. God offers to have that same intimacy, connection, provision, and education to us, His sons and daughters today. Through His "Spirit of adoption" that He has given us and the word that He has written to and about us today,* God has designed for us to learn how to relate with Him as sons and live for Him as sons. To accomplish our education, God has written not just a random compilation of books, but has instead organized a curriculum that is to be followed specifically from beginning to end. This is what studying God's word as a Son is all about: recognizing that curriculum given to us in Paul's epistles and studying through it for the edification of our souls unto godliness.
*Visit the Right Division page for a brief explanation of God's three-fold division of His word and the unique scripture to and about us today.