@ChristinaLinzey That is indeed a very deep question I think it would be accurate, at least I think it would be, to say that Jesus has both been God’s Son eternally and that He became the Son of God in the incarnation because the very term Son of God can have multiple meanings in the Bible. We can infer from the fact that God does not change - is the same yesterday, today, and forever (Hebrews 13:8) that Jesus has eternally been in this relation to the Father.
At the same time, there is a profound mystery in both the incarnation and in the Trinity, so we are dealing here with two of the most profound truths of the Christian faith. While a full answer is probably impossible, I think the below article would help you better understand the Biblical use of the term Son of God.
More specifically, Christ himself receives the title “Son of God” in at least 4 ways.7 He is the “son of God” in the sense that he fulfills the role of (1) Adam, (2) Israel, and (3) David. Yet, beyond being a covenant mediator who supersedes these previous “sons of God,” Jesus is also the (4) divine Son. Clearly, we can see why this title is “sometimes misunderstood.”
More explicit to the title “Son of God,” Luke 1:35 identifies Jesus as possessing no earthly father. Instead, “Jesus is designated as God’s Son because he was conceived by the Holy Spirit instead of by a human father.”
Indeed, what we find in the New Testament is that Jesus is the Son of God in two senses. He is the son of God like Adam, Israel, and David, and he is also God the Son, the second person of the Trinity. This truth brings us to the mystery of the incarnation, but it also resolves the tension we find in the many uses of “son of God.”
In the Gospels, we find Jesus is not only the son of God, according to his humanity; he is the Son of God, according to his deity.