Bart Ehrman explains that Jesus is independently corroborated in several contemporary or near contemporary chronicles.
Bart Ehrman, Did Jesus Exist? The Historical Argument for Jesus of Nazareth (New York: HarperCollins, 2012), 82
All of these written sources I have mentioned are earlier than the surviving Gospels; they all corroborate many of the key things said of Jesus in the Gospels; and most important they are all independent of one another. Let me stress the latter point. We cannot think of the early Christian Gospels as going back to a solitary source that “invented” the idea that there was a man Jesus. The view that Jesus existed is found in multiple independent sources that must have been circulating throughout various regions of the Roman Empire in the decades before the Gospels that survive were produced. Where would the solitary source that “invented” Jesus be?