Why did Jesus come into the world in AD 0 (or was it 4BC)?

No, I won't use BCE and CE, unless you mean the C to refer to Christ, not 'common'. BC "Before Christ" and AD "Anno Domini: in the year of our Lord" are perfectly good universal and appropriate markers for global history, for Jesus Christ is the King of the Universe.

A great question 
I was asked this question in a discipleship class this week and it set our minds running. The only verse we could think of was Galatians 4:4....

"...when the time had fully come, God sent his Son, born of a woman, born under the law, that we

might receive the full rights of sons." 

from which we learn that (a) Christ came at just the right time, and (b) he had to be born under the law. Let's list some reasons from these  two knowns.

(i) All the pointers were in place
How do we know that Jesus is from God? Because he was preceded by multiple prophecies all pointing to him. One thing no human can do is to plant sign posts in history before they are born. All these Old Testament pointers show us, for sure, that Jesus is from God.

(ii) All that teaching about sacrifice sheds light on the perfect sacrifice
It was vital that the images came before the reality, the black and white before the colour, the type before the antitype. Those remarkable Old Testament sacrifices help us to understand the greater sacrifice of Jesus Christ. A male, a perfect male without blemish.

(iii) Millenia of sinfulness reveals mankind's need of a Saviour
If Jesus had come in Genesis 4, the absolute wickedness of mankind would not yet have been revealed to the world. But we have the OT record of wickedness - even religious wickedness - and we can see that there is no human solution to our problems.

(iv) Law shows up the need for grace
The law had to come before grace to show the absolute inability of religion to save us. All the law does is expose and increase our sin. Religion (=obey the law) is useless. A new scheme is necessary to know God and live for him. And that new scheme is the grace of God that has come to us from Jesus.

(v) Sin showed up mercy and love
The millenia of sin reveals the incredible love of God. Every passing century revealed more of the wickedness of mankind and made the patience and love of God to such wretches more and more amazing!

(vi) The right time geo-politically
I guess we can recognise that Alexander the Great had given the world a universal language and Rome universal roads.  This made the progress or advance of the Gospel easy. These empires thought they were serving their own ends but they were serving the Gospel of a sovereign God.

These seem to be some of the reasons Jesus Christ, the Saviour of the world, was born, not in Genesis 4, but in Matthew 2.