In Introduction to Biblical Greek we are working through the first chapter of John with the professor. We were going through the first 18 or so verses looking at the aorist tense verbs that occur there. We came across

John 1:14 Καὶ ὁ λόγος σὰρξ ἐγένετο καὶ ἐσκήνωσεν ἐν ἡμῖν, καὶ ἐθεασάμεθα τὴν δόξαν αὐτοῦ, δόξαν ὡς μονογενοῦς παρὰ πατρός, πλήρης χάριτος καὶ ἀληθείας.

And the Word became flesh and dwelled among us, and we beheld His glory, the glory as the only begotten from the Father, full of grace and truth.

and someone raised a question regarding μονογενοῦς (monogenous). The question was concerned with what “begotten” referred to; as I understood it, the questioner was asking if “begotten” referred to the incarnation or if it referred to an eternal begetting.

At least one believed that monogenous referred to the incarnation—specifically that it was the flesh that was begotten. I certainly think that is a tenable answer. It does not seem that the questions the biblical authors were asking were not the questions of later 3rd and 4th century debates. For the writers to say “only-begotten” does not appear to have any reference to an eternal begetting.

On the other hand, the a few verses later, John states

1:18 θεὸν οὐδεὶς ἑώρακεν πώποτε: μονογενὴς θεὸς ὁ ὢν εἰς τὸν κόλπον τοῦ πατρὸς ἐκεῖνος ἐξηγήσατο.

No one has ever seen God: the only-begotten God, the one who is in the bosom of the Father, that one has made Him known.

We have one who is God and qualified as “only-begotten.” Some manuscripts say “Son” instead of “God” but these manuscripts, despite there being more in quantity, are dated much later. Futhermore, the idea in “the one who is in the bosom of the Father” is one of continual action. In other words, the only-begotten indefinitely was in and is in the bosom of the Father. All this seems to say that “only-begotten” refers to something beyond the incarnation.

I would like to submit that “only-begotten” be looked at another way. Instead of the term referring to some sort of begetting, I think a proper definition would be “unique” or “one of a kind.” Indeed, whether the reference here in John is to a begetting before all time or to the begetting of the incarnation, the Logos is in His preexistence or in His incarnation is unique. One might also consider that for God to beget someone, it does not necessarily need to occur within the idea of human begetting; for something of male gender, to beget could simply mean to be a father to.

I would like to note—and this was pointed out by the one who saw “only-begotten” as a reference to the incarnation—that John 1:1 makes a distinction between God and the Word before the incarnation. There is an aspect where the Word was with God (subject-object distinction) and an aspect where the Word was God.