If Jesus of Nazareth indeed did miracles, healed the sick and raised many dead people, was crucified and was resurrected, then why don’t we have documents by non-Christian authors (Romans or Greeks or others) within His lifetime or within the first century. Many prominent leaders, kings, historians will surely have heard about such unique and wonderful news about Jesus of Nazareth, a miracle worker who raised many dead people and resurrected. Even King Herod got the news quickly about the birth of Jesus of Nazareth, King of the Jews. ( N. B. Yes, prominent figures like Caiaphas were also not mentioned during the first century but Jesus of Nazareth was a completely unique historical person unlike other famous kings or leaders at that time).
Sorry for a somewhat slow response. First of all, Rome was a massive empire. Judaea was a small and very distant province of the huge Roman empire. I am sure that leaders in Rome were aware of the early church and I assume that they had heard about Jesus, but it is not clear that they would have written about Jesus. In fact, the vast majority of everything that ever happened in the Roman empire was not recorded in any document we have access to. Who were the important persons in the province of Illyricum in the third century? What were the religions in England or Gaul in the first century? Who was the governor of the province of Cappadocia in the year 140 AD? Like I said, what we know of ancient history is very spotty. Sure, people heard about Jesus, but that does not mean that they wrote it down, or that we have the document, as only a very tiny fraction of all ancient writings are still in existence today. Yes, King Herod heard about Jesus, but is because Jesus lived in his province of the empire. This does not mean that a Roman author on the other side, literally, of the Empire, would report this event. That Jesus was a unique person in history only became clear over the intervening couple of centuries.
Besides, unlike Caiaphas or other prominent Jews in the first century who are not mentioned by historians, Jesus is in fact mentioned by several persons in the first century. Whoever says differently is wrong. The claim that Jesus was not mentioned by non-Christians in the first century is simply not true! Thallus, a Greek historian mentioned Jesus in the 50s AD. He mentioned the darkness in Jerusalem when Jesus died, falsely attributing it to a solar eclipse. Also, Flavius Josephus mentioned Jesus in his book Jewish Wars in AD 94. In addition, Jesus was mentioned in the Babylonian Talmud either the very late first century or the very early second century (Babylonian Talmud Babylonian Sanhedrin43a-b). In addition, Clement of Rome mentioned Jesus in his letter of about AD 95. Let us add that Paul, Luke, Mark, John, James (the brother of Jesus), Peter and others also mentioned Jesus in the first century. Do they not count simply because they are Christians? Are they automatically false witnesses simply because they were believers (who were, by the way, willing to die rather than change their stories)?