Is it likely that there is an intentional relationship between ἐγένετο in Jn 1:3 and Jn 1:6?

Question

The Gk word ἐγένετο (from γίγνομαι) can mean many things: to come into being (to be born or to be produced), to take place, to become (one of ...), etc. In the beginning of John's Gospel, the word is used in both verse 3 and verse 6, and most translations translate it in different ways. That is, in the translation it isn't visible anymore that it's the same word. For example:

³ πάντα δι' αὐτοῦ ἐγένετο, καὶ χωρὶς αὐτοῦ ἐγένετο οὐδὲ ἕν. [...] ⁶ Ἐγένετο ἄνθρωπος ἀπεσταλμένος παρὰ θεοῦ, ὄνομα αὐτῷ Ἰωάννης:
_{³ Through him [the Word from 1:1] all things were made; without him nothing was made that has been made. [...] ⁶ There was a man sent from God whose name was John. (New International Version)}

- Jn 1:3 and 1:6

Theoretically it would be possible that the author of the Gospel meant to put emphasis on the relationship between the two lines by letting the word reoccur: he would want to show that John the Baptist is one of the things that came into being through the Word.
On the other hand, it's also possible that the word reoccurs accidentally because it's just a word with many meanings.

Is there a way to know if it's likely that the author meant to emphasize a relationship between the verses here?

Answer 1

When Mary received the news from the angel Gabriel that she would receive the Promised Seed, she went "in those days" (Luke 1:39) to see her cousin Elizabeth, who was already pregnant with John the Baptist (Luke 1:44). So John was physically older than Jesus.

Now in John 1:30 we see the perfect tense of γίγνομαι occur as follows. That is, John the Baptist indicates that Jesus "had become" before him, even though he (John) was born before Jesus.

John 1:30 (Greek Text)
³⁰ οὗτός ἐστιν ὑπὲρ οὗ ἐγὼ εἶπον, Ὀπίσω µου ἔρχεται ἀνὴρ ὃς ἔµπροσθέν µου γέγονεν ὅτι πρῶτός µου ἦν.

John 1:30 (NASB w/footnote reading)
³⁰ This is He on behalf of whom I said, “After me comes a Man who has become before me, for He existed before me.”

John is saying that Jesus is greater than him, because Jesus had preexisted John (notwithstanding that John was in fact born before Jesus). The verb γίγνομαι is in the perfect, which suggests completed action in past time with present results. In other words, the "γίγνομαι" of Jesus (described in John 1:3) preceded the "γίγνομαι" of John (described in John 1:6), even though John was physically older because he was born before Jesus. Thus "γίγνομαι" has different interpretive connotations for John the Baptist and Jesus in the Gospel of John.