There are two way in which one can question the Eternal Sonship of the Person of Christ as the Second Person of the Holy Trinity prior to his incarnation. The first way is to join forces with heretics throughout ecclesiastical history and say Jesus is not the eternal Son, because he didn’t exist before his incarnation. Or if he did exist prior to his incarnation, he was and is a lesser created being who had a beginning just as the rest of the creation had a beginning. The second way is to engage with a longstanding conversation within the bounds of orthodox Christianity and say Jesus is not the eternal Son, because the title of the Son is bound to who he is in his incarnation.
From what I can tell, the title of “Son” is indeed bound up in who the Second Person of the Trinity is in his incarnation as true man. The revelation of the Trinity is inseparably linked to the Hypostatic Union of Christ’s two natures in one Person.
A related question is whether the titles “Son of God” and “God the Son” refer to the same thing. Yes, they refer to the same Person. But, no, they don’t refer to the same description of that Person. In the present discussion of eternal Sonship, the title “God the Son” is the sense of the title “Son” being considered. The title “God the Son” refers to the Second Person of the Trinity and is back-projected (as are the titles “God the Father” and “God the Spirit”) from the revelation of the Three Persons in the administration of redemption. But the title “Son of God” has thick precursors in the Old Testament with respect to Israelite Nationhood and the Davidic Kingship.
For all practical purposes, the title “Son of God” in the writings of the New Testament is interchangeable with the title “Messiah” and the office of Davidic King. This contributes to the historical and social context into which the Second Person of the Holy Trinity became incarnate as a man. And this context contributes to the administration through which the Second Person has revealed himself and his relationship with the First Person as the Father. But the question at hand is whether or not this context exhausts the basis for the title of the “Son” (and the title of the “Father” for that matter).
This is not baseless speculation. Theologians have taken a que from the Apostle John in the prologue of his Gospel and observed that “in the beginning was the Word” and that “the Word became flesh” as the Son of God. Talk of Jesus as the “Son” occurs only after the incantation in John’s Gospel. He explicitly gives the Second Person the title of the “Word” in state prior to incarnation into eternity past. This has given theologians reason to think it may be more proper or useful to think of the Second Person as the eternal Word prior to his incarnation as the Son. The Johannine Word can easily be linked with Yahweh’s Word who seems to take on a distinct personality in relation to Yahweh as the Word who expressed himself to and through the ancient prophets.
This issue may not be resolvable, but it’s hardly unimportant. Having this conversation becomes an occasion in which to ruminate on the Person and work of Christ and exult in the gloriousness of the Trinity and the Incarnation. That’s hardly a waste of time!