At the onset, I guess it is essential to state that Son of God is same as God nothing more or less. Son of God is “of God.” The claim to be of the same nature as God—to in fact be God. God took a human birth and that’s how the title “Son” came to him though He was Himself is God. God though divine is revealed in human nature to man. Jesus Christ is the image of God to mankind. God - omnipotent, revealed Himself to mankind, in Jesus Christ.
Here is what Bible says on this:
Jesus gets an answer from His disciples that He is Son of God and acknowledges it affirmatively.
Matt. 16:15 He said to them, “But who do you say that I am?” 16:16 Simon Peter answered, “You are the Christ, the Son of the living God.” 16:17 And Jesus answered him, “You are blessed, Simon son of Jonah, because flesh and blood did not reveal this to you, but my Father in heaven!
John 1:49 Nathanael answered him, “Rabbi, you are the Son of God; you are the king of Israel!” 1:50 Jesus said to him, “Because I told you that I saw you under the fig tree, do you believe? You will see greater things than these.”
Jesus is worshiped by people in His lifetime
In Revelation, an angel instructed the apostle John to only worship God (Revelation 19:10). Several times in Scripture Jesus receives worship (Matthew 2:11; 14:33; 28:9, 17; Luke 24:52; John 9:38). He never rebukes people for worshiping Him. If Jesus were not God, He would have told people to not worship Him, just as the angel in Revelation did.
In these verses Jesus Himself declares it:
John 8:58 Jesus said to them, “I tell you the solemn truth, before Abraham came into existence, I am!”
Jews who heard this statement responded by taking up stones to kill Him for blasphemy, as the Mosaic Law commanded (Leviticus 24:16).
John 10:35 If those people to whom the word of God came were called ‘gods’ (and the scripture cannot be broken), 10:36 do you say about the one whom the Father set apart and sent into the world, ‘You are blaspheming,’ because I said, ‘I am the Son of God’?
Then take for example Jesus’ words in John 10:30, “I and the Father are one.” We need only to look at the Jews’ reaction to His statement to know He was claiming to be God. They tried to stone Him for this very reason: “You, a mere man, claim to be God” (John 10:33). The Jews understood exactly what Jesus was claiming—deity. When Jesus declared, “I and the Father are one,” He was saying that He and the Father are of one nature and essence.
Here Jesus accept this salutation from Thomas for otherwise He would have rebuked Thomas.
John 20:28 Thomas replied to him, “My Lord and my God!”
Jesus affirm that He is Son of God:
Matt. 8:29 They cried out, “Son of God, leave us alone! Have you come here to torment us before the time?”
Mark 3:11 And whenever the unclean spirits saw him, they fell down before him and cried out, “You are the Son of God.” 3:12 But he sternly ordered them not to make him known.
And in this verse, John clearly states that Jesus is true God.
1 John 5:20 And we know that the Son of God has come and has given us insight to know him who is true, and we are in him who is true, in his Son Jesus Christ. This one is the true God and eternal life.