In the Hebrew scriptures the phrase is used in several senses and none of them makes the bearer divine. The oracle to David promises that the king successor will be a son to God and God a father to him, and the enthronement psalm has God say to the king that he is his son, begotten today, which is coronation language. Israel as a people is called God firstborn son in the demand made to Pharaoh. Heavenly beings appear as sons of God in Job and elsewhere. In each case the relation is one of appointment, election or membership of a class, not of shared nature.
That range matters for reading the New Testament, because a first century hearer would not have taken the title as an automatic claim to divinity. The opening of Romans preserves what many scholars regard as an older formula, describing Jesus as descended from David according to the flesh and appointed Son of God in power by the resurrection, which reads as appointment rather than eternal status. The gospels use the title at the baptism, the transfiguration and the crucifixion, at moments of disclosure.
Whether the earliest usage is functional, saying what Jesus does and what office he holds, or ontological, saying what he is, is one of the standing questions in New Testament scholarship, and the answer given tends to determine how the rest of the development is read. What is not in doubt is that by the second century the churches were using the title in the stronger sense.