The Greek word translated "only begotten" (monogenes) is a compound word of monos (one/only) and genos (offspring/kind) and means "only offspring" in every occurrence in the New Testament, and does not prove Christ's begottenness but only his being "the sole offspring" of the Father.
The Word is the "only offspring" of the Father (John 1:14) but all humans collectively are also "offspring" of the Father (Acts 17:28), so is this a contradiction? No. John explains why. It is because the Word is "the only offspring who is God as to his nature" (John 1:18).
In Romans 1:4 Paul wrote that Christ was declared or made known to the world as God's Son with power at his resurrection according to his spirit of holiness, i.e. divine nature (not the third person of the Trinity). Paul is very explicit here; Jesus is "God's Son" according to his divine nature.
In coherence with Romans 1:4, Paul elucidates in Acts 13:33, Hebrews 1:5 and Hebrews 5:5 that Christ was declared, not made, to be "God's begotten" Son at his resurrection.
And Paul adds more; he said that the Son is the "first-begotten" of the Father (Col. 1:15) which is in apposition to the clause which precedes it, meaning, the Son is the uncreated "Image of the Father" (homoousios) as opposed to us humans who were created in the "Image of the Trinity" per Genesis 1:26-27 and hence, heteroousios (of a different substance).
The Divine Wisdom in the LXX Proverbs 8:25 is said to be born by God (Greek genna) before creation.
The Messiah in the LXX Psalm 110:3 is said to be born by God from his womb before creation.
In conclusion, the Apostle Paul explains the Sonship of the Word by his "birth" and John elucidates it by his being the "only offspring" of the Father. Both metaphors prove that the Word is consubstantial with the Father. The Word is the only offspring of the Father, birthed by him and hence, equal to him in nature, or as the Nicene Creed puts it "only begotten, born not made, of one nature with the Father."