No, what is translated "only-begotten" means to be uniquely existent.
Now the Son of God was always the Son of God, not caused to be the Son of God.
Is the same YHWH as the Father though they are different persons.
John 1:1-2 teaches the Word to be bothwith God and was God.
I have repeatedly
made that clear.
What is with God is someone other than God.
And what was God would always be God.
And according to John 1:3 is the sole cause of all caused things.
John makes it explicit, the Word was with Godtwice, ". . . was with God, . . ." -- John 1:1. And ". . . with God. . . ." -- John 1:2.
The Word being someone other than God.
And ". . . was God," too. John 1:1.