"There is no proof. Only what was written by those "guys." "
Jesus was mentioned by two independent sources outside of the Gospel writers. The Jewish historian Josephus included both him and John the Baptist in his history of the Jewish people that was published late in the first century.
The Roman historian Tacitus also included a reference to the Jesus's execution, ordered by Pilate. This was published early in the second century.
Now, of course, both of these historians were born after Jesus's death, so they are still not first-hand witnesses or accounts, but they are both considered significant as sources from outside of Christianity that there was a man named Jesus who was baptized by John the Baptist (as recorded by Josephus) and was executed at the hands of Pontius Pilate (recorded by both Josephus and Tacitus).