No, there are no historians (which I think is what you meant) or historic notification, which proves that Jesus Christ really existed on earth, from a time when Jesus was alive. All such accounts were from long after Jesus lived.
But that does not mean there was no Jesus. The problem is that the Jesus of the NT is a result of myth building in the years after Jesus was executed.
The fact is that Jesus was a Jew and died a Jew. He had no thought of bringing about a new religion, only in helping to fulfill his own religion. He certainly would have been horrified if he had learned that a new religion would be formed with him as its basis and that it made a deity of him.
Jesus was proclaiming that god would imminently overturn the existing order and establish a new kingdom--the kingdom of righteousness.
And the Romans executed him because they perceived him to be a rebel who was seeking to establish a new kingdom. That is why they placed the placard saying "The King of the Jews" on the cross. They wanted him to be an object lesson to those who would seek to overthrow them and establish a new kingdom.
By the time the gospels were written, there had been a schism between the original Jewish followers of Jesus and those who followed Paul, who was the actual originator of Christianity. Paul brought in many esoteric and pagan ideas and added them to the myths about Jesus that had developed in the years following his execution. Paul also expanded his church by preaching to and bringing in Gentiles, who did not hold any particular allegiance to the Jews.
In addition, the Christian church at the time was trying to make their way in the hostile Roman world, and they did not want to antagonize the Romans (see Romans 13:1-2), so they minimized the Roman involvement in the death of Jesus and laid the blame on the Jews, which furthered even more the separation of the new religion from its Jewish roots.
That resulted in the origin of Christianity.
Here is some relevant material relating to the above.
There is no contemporary account of Jesus at the time he was living. Even the New Testament accounts were written after his death. As far as non-biblical sources, all the Christians can do is to refer to documents that were written long after he died.
It was only several years after his death that his followers eventually became numerous enough and influential enough that he became more well known. By then, the myths that had developed about him after his death magnified his persona and made him something he wasn't.
The trial of Jesus by Pontius Pilate was a later fabrication by the Christian leaders that they devised, by blaming the death of Jesus on the Jews, to prevent their followers from instigating actions against the Romans. Pilate was a Roman official and he was hardly the kind of person he was made out to be in the gospels. He would have had no compunction against condemning Jesus as a rebel. In fact, if he had let Jesus go free, he would have had to answer to his superiors for not condemning a rebel against their authority. As Josephus makes it clear, Pilate was arrogant and brutal as procurator. See also Luke 13:1.
The Jewish leaders could have had Jesus executed if they found cause to do so. They did not need to turn him over to the Romans to be executed. Read Acts 6:5-15 and Acts 7:54-60, which clearly indicates that the Jewish leaders could have those they condemned to death executed without the need to turn the condemned over to the Romans. The claim that they did not have the authority to execute those they condemned to death, and that was the reason they turned him over to the Romans, was a later fabrication to lay the blame for the death of Jesus on the Jews and to explain why the Romans, rather than the Jews, executed him.
The fact is that the Jewish authorities did not have cause to execute Jesus. Jesus did not actually claim to be god-- that claim was one of Paul's additions to the myths about Jesus, and the writers of the gospels wrote them accordingly by putting words into the mouth of Jesus.
So what it boils down to is that Jesus was executed solely for being a religious agitator who was proclaiming god's imminent overthrow of the existing order, and not because of the later fabrications that were added to his message.