Craig A. Evans writes in “Jesus and the Dead Sea Scrolls in Qumran Cave 4” that,

“…there can be little doubt that the prominence in the New Testament of the epithets such as ‘Son of God’ and ‘Son of the Most High’ probably has something to do with their usage in the Graeco-Romans world. These and closely related epithets were everywhere applied to the Roman emperors. One inscription describes Julius Caesar (ruled 48-44 BCE) as “the manifest god from Mars and Aphrodite, and universal savior of human life” (SIG 760). In many inscriptions and papyri Augustus (30BCE-14 CE), who was emperor when Jesus was born (ca. 4-5 BCE), is frequently called “God” and “Son of God” (e.g., POxy 257; POxy 1266; POslo 26). Tiberius (14-37 CE), who ruled the Roman Empire when Jesus was crucified (ca. 30 or 33 CE), called himself the “Son of God” and the “Son of Zeus the Liberator” (SB 8317; POxy 240). Nero (54-68 CE, who ruled when the Gospel of Mark was being written, called himself “the Son of the greatest of the gods” (IM 157b) and “Lord of the whole world” (SIG 814). Similar language was used in reference to Emperor Vespasian (69-79 CE, who ruled the Roman Empire when the Synoptic Gospels were composed and began circulating among Christians.”

In Craig A. Evans and Peter W. Flint (eds), Eschatology, Messianism, and the Dead Sea Scrolls (Grand Rapids: Wm. B. Eerdmans, 1997), p. 93.

Evans goes on to note that 4Q246 shows that this epithet was not exclusive to the Graeco-Roman milieu (p. 94). This text from Qumran mentions a king (likely Davidic) who will be called “Son of God” and “Son of the Most High.” This text mentions his kingdom as being everlasting, which again is Davidic.

We should recognize that “Son of God” has flexibility of definition. When used in a first century Jewish context it likely had to do with a Davidic heir who would restore Israel’s kingdom. But as the people of the empire heard it there is no way they could avoid comparing the claims to those of the Caesars and their supporters.