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I think our safest and most reliable course of action is to see how the term is used and understood in the New Testament. Here are the references to “Son of God” in the NT:
Matt. 4:3; 4:6; 8:29; 26:63; 27:40; 27:43; 27:54
Mk. 1:1; 3:11; 15:39; 1:35; 3:38; 4:3; 4:9; 4:41; 22:70
Jn. 1:34; 1:49; 3:18; 5:25; 10:36; 11:4; 11:27; 19:7; 20:31
Acts 8:37; 9:20
2 Co. 1:19
Heb. 4:14; 6:6; 7:3; 10:29
1 Jn. 3:8; 4:15; 5:5; 5:10; 5:12; 5:13; 5:20
It is interesting to note that Satan, in the temptation of our Lord (Matthew 4:3, 6; Luke 4:3, 9), challenged Jesus on the basis of His being the Son of God (the “if” here does not cast doubt on this fact, but is used in the sense of, “since you are. . .”). I believe that here Satan is challenging Jesus to (mis)use His power and authority as Messiah. = “You are the Messiah, so let’s see you act like it.”
The demons, too, referred to Jesus as the “Son of God” (Matthew 8:29; Mark 3:11; Luke 4:41). The text in Luke is most enlightening:
Demons also came out of many, crying out, “You are the Son of God!” But he rebuked them, and would not allow them to speak, because they knew that he was the Christ.
Notice that being “the Son of God” was the same as being “the Christ” – the Messiah.
I think it is safe to say that in nearly every instance in the New Testament, being the “Son of God” meant our Lord was the Christ, the Messiah (see John 1:49; 11:27).
There are hints, however, that as the “Son of God,” Jesus was more than a mere man, a mere “son of David,” who would sit on the throne of His father, David. This is especially clear in the Gospel of John, beginning in chapter 5. It also seems to be clear at the trial of our Lord. When Jesus was asked by the priest if He was the “Son of God,” He admitted that He was, and was charged with blasphemy – claiming to be God (see Matthew 16:63, 65, 68).
In the Old Testament, the coming Messiah, the descendant of David, was to become God’s “son” (2 Samuel 7:12-14a; Psalm 2:7). To be God’s “son” was to be the ruler God had appointed, of the line of David. As Israel’s Messiah, Jesus was the “Son of God.” But Jesus further clarified the matter, demonstrating that He was indeed, God manifested in the flesh, something John is eager for His readers to grasp at the beginning of his Gospel (John 1:1-5, 9-14).
Thus, the first century Jew understood the term “the Son of God” to mean “the Messiah.” And with our Lord’s further claims (John 5, 8), they understood this term to mean that Jesus, as the “Son of God” was not only the Messiah but God incarnate.