No One Wrote About Jesus During His Lifetime

Questions about how to respond to the concern that no one wrote about Jesus during his lifetime, why scholars say Jesus was born in AD 5–6 rather than AD 1, and what Paul meant when he said God sent his son “when the fullness of the time came.”   What should I say to someone who is hung up on the fact that no one wrote about Jesus during his lifetime? If Jesus’ birth started AD 1, why do scholars say he was born in AD 5–6? Paul says in Galatians 4:4–5 that God sent his son “when the fullness of the time came.” What was “just right” about that point in history, and is God doing anything special in our day?