I think that as Christians we can confidently answer that according to God's word,
We know that Jesus is the Son of God.
John makes it clear that Christ is the son of God, eternally begotten (John 1:1, 14, 18 and John 3:16, 18). The Father and the Son have always been and have always been in this Father/Son relationship. Any other reference to a child of God is in the sense that one becomes a child of God.
But Jesus is not our brother.
John records Jesus making the distinction that He is from Heaven and we are from this world in John 3:31-32 and John 8:23. Colossians 1:16 tells us that Jesus is the creator of all things including the angels and us as well, “For by him were all things created, that are in heaven, and that are in earth, visible and invisible, whether they be thrones, or dominions, or principalities, or powers: all things were created by him, and for him:”
We were made by God. We are His creation, not His offspring.
We read in Genesis 1:26-27 that we are God's creation and valuable by being in His image (Genesis 9:6). Genesis 2:7 says, "And the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul." Unfortunately, due to sin, a once beautiful creation had become the enemy of God. Genesis 6:6-7 tells us that God was saddened at how quickly His creation had gone bad and so He wiped much of the canvas clean by the waters of the flood.
So where do we get the idea that we are the children of God?
100% of the time when we see God refer to His children in the Bible it is in reference to believers; followers of God. We see this prior to the flood with the line of Seth, later with God's chosen people, Israel (Hosea 1:10), and in the New Testament with believers in Christ (John 11:51-52, Psalm 82:6 - speaking about righteous judges appointed by God, Romans 9:26 - speaking of Israel, Revelation 21:7 as well).
1 John 3:10 tells us that there are many who are not children of God. Jesus declares in John 8:42-47 to those around Him that, "If God were your Father, ye would love me: for I proceeded forth and came from God; ...Ye are of your father the devil, and the lusts of your father ye will do. He was a murderer from the beginning, and abode not in the truth, because there is no truth in him. ...And if I say the truth, why do ye not believe me? He that is of God heareth God's words: ye therefore hear them not, because ye are not of God." Paul says in Ephesians 2:3 that man is by nature a child of wrath. The writer of Hebrews says in Hebrews 12: 5-9 that if God is not active in our lives, disciplining us, then we are bastards, and not sons.
We become children by faith.
John 1:12 says that when we believe on His name, He gives the power to become the sons of God. Galatians 3:26 says that we "are all the children of God by faith in Christ Jesus."
We are adopted into the family of God.
Romans 8:15 For ye have not received the spirit of bondage again to fear; but ye have received the Spirit of adoption, whereby we cry, Abba, Father. Paul equates adoption with redemption in Romans 8:23 and in Galatians 4:5 says, "To redeem them that were under the law, that we might receive the adoption of sons." Ephesians 1:5 tells us that it pleases God to choose His children for adoption through Christ like He chose Israel (Romans 9:4).
Why would we need to be adopted into God’s family if we were already His children?
Only the saved are called children of God.
1 John 3:1-2 tells us, “Behold, what manner of love the Father hath bestowed upon us, that we should be called the sons of God: therefore the world knoweth us not, because it knew him not. Beloved, now are we the sons of God, and it doth not yet appear what we shall be: but we know that, when he shall appear, we shall be like him; for we shall see him as he is.” Jesus says in Matthew 5:9, “Blessed are the peacemakers: for they shall be called the children of God.”
Why would we have to now be “called” the sons of God, if we were already His children?
Our status as children of God is synonymous with forgiveness (Romans 8:21), salvation (Philippians 2:15, Romans 9:8, Luke 6:35, Luke 20:36), being in Christ (1 John 5:2 – here John is speaking about the body of Christ) and filled with the Holy Spirit (Romans 8:14, 16).
What about Acts 17:28-29?
I find it interesting that when talking with LDS about this subject, they almost always point to this verse to prove that everyone is literally a child of God. The problem is that Paul is using Pagan ideas as a springboard for pointing toward the true God similar to how he uses the altar of the “unknown God”.
I think that as Christians many times we aren't clear about this distinction and perpetuate the myth that every created person is a child of God. As a painter sees fit to create, and if not satisfied, start his painting anew, so God has the right with His creation. While we are certainly created in God's image, but we are made family by adoption and heirs with Christ by faith in His redemptive work by God's grace.