Let’s assume this is about Christ and not David, or if it was David as a Type of Christ, then it is still is about Christ, so we must accept Christ is in time born as a Son in some way. First off then obviously ‘Today I have begotten thee’ must be referring to the ‘humanity’ of Christ, not his ‘divinity’ as God, the eternally begotten Son proceeding from the Father without beginning.
Second, it does not really matter if one interprets this declaration of Christ’s humanity as becoming ‘a Son’ at his a) incarnation, b) his baptism by John, or c) his resurrection, as it all amounts to his human nature in either case being declared to being made a Son. (Personally I like the incarnation as my first pick Luke 1:35, but he was declared to be the Son in power on his resurrection, and a voice from heaven did declare it also in his Baptism, so I can accept any of them, yet seems best to stick with science as he was literally born a son in a virgin’s womb).
Third, it might be helpful to understand that the humanity of Christ was predestined to be made a Son of God ‘for us’, in order that we too by being united in him would be adopted sons.
For he chose us in him before the creation of the world to be holy and
blameless in his sight. In love he predestined us for adoption to
sonship through Jesus Christ, in accordance with his pleasure and
will— to the praise of his glorious grace, which he has freely given
us in the One he loves. Ephesians 1:4-6 NIV
This means God the father before the creation intended to make the God-Man in order to adopt us and make us sons. By taking upon himself a human nature, God made Jesus a unique and only natural created son. He was not adopted or brought into his sonship indirectly through any law but God created the humanity in a virgin directly, being made his natural son. Just as Adam was a natural son as God made him directly. We on the other hand were created indirectly but our new creation through being united to his humanity and having been justified are reconciled to God in his death and resurrection, made us adopted sons only.
Just as he was fashioned into our image to save us, we are fashioned into his image through new birth. Jesus is a Son, therefore we are a son. Jesus was made a king, therefore, we are a kings. He possess all things. We posses all things. We are formed into his image and become sons, not directly but in him we are adopted and made sons. He is the head we receive his benefits only as members of his body.
So what was Jesus’s relationship before he was a Son?
The question is somewhat confusing because before the man Jesus was born he had no physical existence and so one can’t ask “what his relationship to God was’ - he obviously did not exist. However, before the creation of his humanity, God the divine Son who had no beginning, being eternally begotten of the Father was predestined to assumed this human nature called ‘Jesus’ and this union would make the promised ‘Christ’ or God-Man, having two natures and only one personality. Therefore, his human nature he was eternally elect and predestined to be created, as the only natural Son of God by the Holy Spirit in a Virgin’s womb. Jesus, the man, was ‘made a Son’ in this way, by being assumed by the Eternal Son. This election, of creating a human Son, to be united with the Eternal Son, was destined in order to adopt the rest of the elect (his body) in him. In other words, the human nature of the Christ, the man Jesus, had the relationship to God as being predestined to be made his son (i.e being made one with the second person of theTrinity) before the creation of the whole universe.