Is it true?
Did Jesus really exist?
Almost every historian of the ancient world says yes, including many who are not Christians.
Some people say Jesus never lived. That is not what historians think. Among scholars who study the ancient world, Christian or not, the view that Jesus never existed is treated as a fringe idea.
Bart Ehrman is a good example. He is a leading New Testament scholar and an agnostic, and he wrote a whole book to say that Jesus certainly did exist. Scholars argue about what kind of teacher Jesus was. They do not seriously argue about whether He lived.
Besides the New Testament, a handful of Roman and Jewish writers from the first and early second centuries mention Jesus or His followers. None of them were Christians, and some were openly hostile. For a man from a small village in a far corner of the Roman Empire, that is a lot of evidence.
These sources do not prove anything about faith. They show something simpler: Jesus was a real man, executed under Pontius Pilate, whose followers kept going after His death.
Scholars agree He lived
Virtually all scholars reject the theory that Jesus never existed. Bart Ehrman, an agnostic, wrote Did Jesus Exist? (2012) to argue that whatever else you think about Jesus, He certainly did exist.
Sources
Tacitus, Roman historian (about AD 116)
Writing about Nero blaming Christians for the fire of Rome in AD 64, Tacitus says their founder Christus was executed under Tiberius by the governor Pontius Pilate (Annals 15.44). Most scholars see the passage as genuine. He does not name his sources, so some ask whether he relied on what Christians said.
Sources
Josephus, Jewish historian (about AD 93-94)
Josephus mentions Jesus twice in his Antiquities of the Jews. The longer passage (18.3.3) has clearly been edited by later Christian copyists; most scholars think Josephus wrote a shorter, neutral original about Jesus that was later added to, while a minority think the whole passage was inserted. The second passage (20.9.1) names James as the brother of Jesus who was called Christ, and is almost universally accepted as genuine.
Sources
Pliny the Younger, Roman governor (around AD 110)
As governor of Bithynia and Pontus, Pliny wrote to Emperor Trajan asking how to deal with Christians. He reports that they met before dawn and sang a hymn to Christ as to a god (Letters 10.96). Scholars regard the letter as authentic, though one recent study suggests parts of the text were added later.
Sources
Suetonius, Roman biographer (early second century)
Suetonius says Nero punished the Christians, and that Claudius expelled Jews from Rome over unrest stirred up by someone called Chrestus. Scholars disagree on whether Chrestus means Christ, so this one is weaker evidence.
Sources
The Talmud (handle with care)
Some later Jewish writings mention a Yeshu who was executed on the eve of Passover. They were written down centuries later, between roughly the third and fifth centuries, and scholars disagree on whether they refer to Jesus of Nazareth at all. Most do not treat them as reliable history about Him.
Sources
My verses
Many have undertaken to compose an account of the things that have been fulfilled among us, just as they were handed down to us by the initial eyewitnesses and servants of the word. Therefore, having carefully investigated everything from the beginning, it seemed good also to me to write an orderly account for you, most excellent Theophilus, so that you may know the certainty of the things you have been taught.
In the fifteenth year of the reign of Tiberius Caesar, while Pontius Pilate was governor of Judea, Herod tetrarch of Galilee, his brother Philip tetrarch of Ituraea and Trachonitis, and Lysanias tetrarch of Abilene, during the high priesthood of Annas and Caiaphas, the word of God came to John son of Zechariah in the wilderness.
For the king knows about these matters, and I can speak freely to him. I am confident that none of this has escaped his notice, because it was not done in a corner.
For what I received I passed on to you as of first importance: that Christ died for our sins according to the Scriptures, that He was buried, that He was raised on the third day according to the Scriptures, and that He appeared to Cephas and then to the Twelve. After that, He appeared to more than five hundred brothers at once, most of whom are still living, though some have fallen asleep. Then He appeared to James, then to all the apostles. And last of all He appeared to me also, as to one of untimely birth.
Only after three years did I go up to Jerusalem to confer with Cephas, and I stayed with him fifteen days. But I saw none of the other apostles except James, the Lord’s brother.
Further reading
Links open independent sources, not church websites.