According to most New Testament scholars, the Greek term translated "begotten" in John 3:16 was improperly translated. The correct translation should have been "only Son" or "unique Son." For example, in the NIV the verse reads:
For God so loved the world that He gave His one and only Son.
This passage and others ( John 1:14,18; 3:18 ; 1 John 4:9 ) that refer to Christ as "begotten" don't imply that the doctrine of the triune God is wrong, nor do they imply that Christ doesn't have eternal existence. These passages refer specifically to the incarnation, the unique occasion in which God became a human being. While Christ has existed from eternity, the incarnate Son of God came into existence at a specific time in history.
An early heresy within the church maintained that the Son was not co-eternal with the Father but was a created being (although of a higher order than other created beings). This heresy (Arianism) wasn't based on Scripture but on philosophical and rationalistic objections to the Bible's teaching about the incarnation and the tri-unity of God. The Council of Nicaea (AD 325) was formed to deal with Arianism and declared that the Son was "begotten, not made," and "of one substance" with the Father (that is, of the same nature or essence with the Father).
The Bible says that the Word (logos) was God and existed before creation ( John 1:1-2 ). Then it identifies that Word as Jesus, the one who "became flesh and made His dwelling among us" ( v.14 ). Jesus Himself declared His preexistence in such passages as John 8:58 and John 17:5 . On numerous occasions, the New Testament writers identified Jesus with Jehovah ( Luke 1:76 ; John 10:30; 14:10 ). And many other passages uphold Christ's preexistence and involvement in creation ( John 1:1-3; 5:18; 10:30 ; Romans 9:5 ; Colossians 1:15-16 ; 2 Thessalonians 1:12 ; Hebrews 1:2-3 ; 2 Peter 1:1-2 ; 1 John 2:22-23 ).