How and when did Jesus make us children of God?

A child of God is righteous and is part of God’s holy family. First consider different examples of sons of God. Angels are sons of God. Job 1:6, “Now there was a day when the sons of God (angels) came to present themselves before the LORD, and Satan came also among them.” Additionally, when Adam was created perfect and sinless, he was a son of God. Luke 3:38 (NLT), “…Seth was the son of Adam. Adam was the son of God.”  But Jesus was the “only begotten Son” (John 3:16 KJV), that is Jesus was directly begotten by God. After the Logos (Jesus in His prehuman existence) was created; the Logos served as God’s instrument to make the rest of the creation. 1 Corinthians 8:6 (ESV), “there is one God, the Father, from whom (by His plan) are all things and for whom we exist, and one Lord, Jesus Christ, through whom are all things and through whom we exist.”

How and When could we be made children of God?

After Jesus completed his ransom sacrifice, the way was open for people to become sons of God again. God invites us to “…enter the Holiest by the blood of Jesus, by a new and living way which He consecrated for us…” Hebrews 10:19, 20. Please note: it is a new way opened by His blood.

To enter this way, one must become a Christian. He needs to recognize he is a sinner and accept Jesus as his savior. Acts 4:12, “Nor is there salvation in any other, for there is no other name … by which we must be saved.” Then he must deny his own will to do God's will. “Then said Jesus unto his disciples, If any man will come after me, let him deny himself, and take up his cross, and follow me.” Matthew 16:24.  God demonstrates His adoption of this person into His family by begetting him with the holy spirit. “The Spirit you received brought about your adoption to sonship. And by him we cry, ‘Abba, Father.’” Romans 8:15 (NIV) Thus, we become children of God when we receive the Holy Spirit.

Were people born before Jesus ever called sons of God? No. The Jews under the Law were privileged to have a covenant relationship with God but Paul called them servants. Galatians 4:7, "Wherefore thou (Jews) art no more a servant, but a son (as  a Christian)…" When Jesus was addressing His followers He elevated them from a servant to a friend of God. “No longer do I call you servants… but I have called you friends, for all that I have heard from my Father I have made known to you” John 15:15 (ESV). The rest of the world are called “children of wrath” Ephesians 2:3.