Yes, He did exist before but not as an Angelic being but as The WORD in the form of invisible Spirit - expressing in duality of powers. That's why YHWH is also presented as a Man - Exod 15:3 and even before in Gen 3: 8 - YHWH walking in the Garden and also having a voice.Paul specifically notes that Christ comes from the Fathers "according to the flesh". The implication is that Jesus existed before he became human. (And Paul makes this clear in some of this other epistles.) If he had omitted the phrase "according to the flesh" the meaning of the passage could be understood in the manner you suggest.
What does John in his gospel mean that no one has seen God at any time. Why does Paul say that there is a image of The INVISIBLE GOD? Why did Christ tell the Jews that they have never seen The Father's form nor heard His voice?
This is the clue that God operates in two distinct dimensions - Transcendence and Immanent creation.
Because these distinctions are not acknowledged in Christendom, there is so much confusion over Theology and Christology.
John 1:1 provides distinction - God and The WORD. John's context of the whole chapter is about The WORD and not The God He was with. God is utter transcendent.
He also shows that God is one and The WORD is not another distinct Person called God. He is One but works in two dimensions. If this is not understood then there will be total confusion and arrive at false doctrines that are rampant in these boards. No knowledge of Biblical languages will ever lead anyone to truth but it's The Spirit behind the scriptures matters. The ample evidence of confusion between the posters is the disagreement despite reading the same language. This shows that something must be wrong. Instead of showing some humility, each one trying to demonstrate their superiority over the languages. This should end.
The titles - Father and Son is only relevant to covenant relationship with Israel. Israel is the heir to the promises of God as first the gospel message was taught to Abraham when he was a heathen. His crossing over after his calling makes him a Hebrew. It's not that gospel message wasn't there before him (Gen 1:2-3) but God was working towards building His Assembly (as Adam and Eve taken out of him prefigured) which is Israel built from 12 tribes. There was however falling and rising of many in Israel as it was transitioning from fleshly elements of Torah of sin and death to the Torah of the Spirit of life in Messiah (New Covenant).
So Messiah not only came to represent Israel as the firstborn Son but also mediate for Israel. - Exod 4:22; Hos 11:1; Mat 2:15; Gal 4:1-4; Rom 8:29 and more.
These scriptures and many more show the evidence that Messiah came as a representative and Mediator of Israel. He came by His own choice - Heb 2:11-16.
Btw, Who spoke as The Father of Israel in OT when God is utter transcendent? Why was there a need for YHWH to reveal Himself in duality of powers in OT.
The same is true in the NT. As the Ordinal First, He is The Father and as the Ordinal Last, He is The Son. - The Aleph and Tav.
Anyway, The Son will be subject to the Father at the end of the age (1Cor 15:28) as All Israel would have been delivered and He will establish His Tabernacle with men - Rev 21:3; 7.