The word used for “begotten” in this sense, is not fabricated and being added to the Bible’s concept. The word “monogenes” is used in the sense of being unique or one of a kind son within a specific relationship and is not being used in the sense of “coming after”. The same word is used in Hebrews 11 when speaking of Isaac. Calling Isaac Abraham’s only begotten son but we know that Isaac was NOT Abraham’s only son but rather his unique one of a kind son, i.e., the son of promise.
In the Bible this relationship is described and played out on many passages, He is the Word (look up “The Memra”) or Son who is none other than God in the flesh. When Jesus says no man has ever seen the Father, the only begotten son has declared Him, this means that He has made Him manifest. So though we cannot see the Father, when we see and hear the Son we are seeing and hearing GOD who we think of as “the Father”.
God has the intention of having many sons of whom the man Christ Jesus is the model, the source, and the means. It is only by and through the Son that we may know the Father. IN HIM we are a new creation, not merely of the old Adam, but born from above after the order of the last Adam (Christ) having both a temporal existence and eternal life. We are then said to be in the world but not of it.
The Word, or Son, is the perfect reflection of the Father, otherwise God is totally transcendent (beyond comprehension) and unknowable personally. All through the Old Covenant writings (in many forms), as well as in the New (while in the flesh), it has always been the Son, or Word, that revealed, or unfolded, or made manifest, the Father, His words, and His works to mankind.
John the Baptist bears witness to this understanding in John 1:18 (read this). YHVH, the God of Abraham, Isaac, and Jacob, the one who revealed Himself to them and so many others in so many different ways (Genesis 18-19; Exodus 3; Joshua 5:13-15; Judges 13, etc.,), became flesh and dwelt (tabernacled) among us (John 1:14). One could almost say YHVH the Son is YHVH the Father’s “image” of Himself, although that would fall short as well. Why? Because the One and Only (Yachid, or unique, one of a kind) God is also “one” in a different sense (He is echad or Unity). This is what is meant when in Deuteronomy 6:4 Moses declares the axiom of our monotheism, “Hear o’Israel, the Lord our God (Yachid is here implied), the Lord is one” (the word echad or Unity is used). Parenthesis mine. See also John 17.
As God is only one (yachid) in essence, substance, and nature, the three eternally distinct persons of the Godhead (Father, Son, and Holy Spirit) are also the one (echad) God, thus all (echad) are the eternal (yachid), without beginning or end. Thus the name “He who is”, or as we translate it “I AM”, to imply the uncreated One who is continuous existence. Theologically, it has been said in our inadequate human terms, that the Son eternally proceeds from the Father (kind of like the glow of the flame), where the Spirit proceeds from the Father and the Son (like the effectualness of the light and heat thereof).
Forgive us Lord for our finite ineptitude to fully articulate your majesty.
Thus it is said of the Son in Hebrews 1 as well as in John 1, that He is “the brightness of His (the Father’s) Glory, the express image of His person” (lit. substance). Parenthesis mine. And incarnate as Y’shua/Jesus he is the perfect “image of the invisible God” (John 14:7; Colossians 1:15; 2 Corinthians 3:18). In character, word, and deed, He is the heart of God toward man. (parenthesis mine)
The phrase ONLY BEGOTTEN is merely the English translation, through the German, through the Latin, from the Greek. When you get that there is only one God and as persons understand that the SON is the brightness (see-able experience-able perfect reflection) of His substance (translated "person"), that "the Son" is also the visible image of the invisible God (that aspect of God that can be known to His creation), then it makes perfect sense.
As long as the limited human language hooks SOME into only understanding "begotten" as something being "born" after something that came first, one has the conflict....God IS...in the eternal there never was a "time" when the Father has not always "generated" or been present with the Son/Word....it has always been the nature of God to make Himself knowable...and some aspect of God's nature IS knowable (but it is puny and finitely grasped by the most knowledgeable intimately related mere human)...but thanks be to God that is as it is as limited as that is....
Again....(forgive me Lord for our linguistic limitations)...Augustine made (forgive us Lord) comparison to the Sun....
There is only one SUN...the essence of the Sun can only be conjectured and speculated on (like the Father) but then because we can see the sun by its flaming (the Son or Word by which/whom God communicates Himself TO His creation) and the heat and light which is effectual in and for us (the Holy Spirit)....
The moment there is "SUN" there is its essence, flame, and effect....there is NEVER a time when the one is not all three nor when all three are not one....that which can be manifest is always being generated...it is one nature to be all three which are not only corporately one but in fact also numerically one....
THEREFORE....in one sense the Son/Word IS the eternal begotten-ness and IS so before all ages
in another sense He is "begotten" or born in time after the worlds were made