Do we have any scientific proof that Jesus existed or is it just our faith?
Sure, there's mountains of evidence for the historical life of a man named Jesus of Nazareth. (Interestingly enough, no one ever seems to have denied the historicity of Jesus until around the 18th or 19th centuries.) In particular, there were a number of writers in ancient Rome and Israel, who lived at the same time as Jesus or shortly thereafter, who wrote on the man-vs.-God controversy while it was first going on. I won't go through all of them, but here are a few notes:
One of the most famous of these writers is Flavius Josephus, a historian born A.D. 37. A Pharisee, he commanded the Jewish forces fighting against their Roman conquerors in A.D. 66, and was captured when Galilee fell and Jerusalem was razed. In The Antiquities of the Jews, xviii.3.3, written around A.D. 93 or 94, he wrote:
"Now there was about this time Jesus, a wise man, if it be lawful to call him a man, for he was a doer of wonderful works, a teacher of such men as receive the truth with pleasure. He drew over to him both many of the Jews, and many of the Gentiles. He was the Christ, and when Pilate, at the suggestion of the principal men among us, had condemned him to the cross, those that loved him at the first did not forsake him; for he appeared to them alive again the third day; as the divine prophets had foretold these and ten thousand other wonderful things concerning him. And the tribe of Christians so named from him are not extinct at this day."
An Arabic translation of this passage reads:
"At this time there was a wise man who was called Jesus. And his conduct was good, and (He) was known to be virtuous. And many people from among the Jews and the other nations became his disciples. Pilate condemned Him to be crucified and to die. And those who had become his disciples did not abandon his discipleship. They reported that He had appeared to them three days after his crucifixion and that He was alive; accordingly, He was perhaps the Messiah concerning whom the prophets have recounted wonders."
Another ancient historian was Cornelius Tacitus, born sometime between A.D. 52 and 57 (no one seems to agree on this). He was the Roman governor of Asia and the son-in-law of the governor of Britain, and to him we owe much of our knowledge of the Roman emperors, including Tiberius, Claudius, and Nero. In his Annals, first dating from around A.D. 117, he wrote:
"Christus, the founder of the name [Christians], was put to death by Pontius Pilate, procurator of Judea in the reign of Tiberius." Annals xv.44
Justin Martyr, born A.D. 100 in Palestine, called himself a Samaritan but was probably of Greek or Roman ancestry. A well-educated philosopher, he studied the doctrines of Plato, Aristotle, Pythagoras, and the Stoics, but decided Christianity was the only philosophy that was "safe and profitable." When forced to defend his beliefs to the Emperor Antoninus Pius, he referred the emperor to the report written by Pontius Pilate at the time of Jesus' crucifixion for details of the incident--a report which Martyr presumed must have been on file in the imperial archives but which has unfortunately been lost through the centuries. Martyr, of course, was killed for his beliefs.