We can never know the past with certainty, for we can have no direct experience of it. Let us take an example. Did Julius Caesar exist? We have the word of ancient Romans that he did, but we have no body, as he was cremated. So how can we know that there was not a vast conspiracy to pretend that he did in fact live? We cannot, but what we can do is create a coherent picture of the world, using reports from the past, as if we were doing a jig saw. Slowly by eliminating inconsistencies we create a picture that seems meaningful and rational, and this we believe to be the true picture. In Caesar's case there is no meaningful picture of the past that excludes his existence.
It is the same with Jesus of Nazareth. As with all historical knowledge we work by inference. We gather data together and interpret it. Often this is an ongoing process in which we are constantly obliged to revise our views, as new data is discovered. History is an attempt to create an accurate picture of the past by the use of inference; and there is no credible picture that excludes Jesus' existence.
Those who deny the existence of Jesus have to deal with one undoubted fact: no one in the ancient world, not even his enemies, denied that Jesus existed. They may have thought him insignificant, they may even have thought him a wrongdoer, but the ancients spoke of him as a person who really existed. Jewish writings also mention Jesus as a historic person, as they state that he was executed for sorcery. These writings found in the Talmud are relatively late, but they confirm that the ancients were convinced that there was really a person called Jesus of Nazareth and that he was somehow linked to Christianity. The ancients were neither stupid nor gullible. Just like us they constructed their picture of the past in a reflective way, and throughout the history of the ancient world their picture of the past never included the belief that Jesus was fictional.
We also have the question of the historicity of the gospel accounts. Few scholars would think that the gospels are purely factual history, but to go the other way and say that there is no truth in them is to make the mistake of thinking in polar opposites. The gospels were written by people who loved Jesus and wanted to preserve his memory. Not all their recollection would be accurate, and it was shaped by the post-resurrection faith of the church, but to think it all false is as erroneous as to think it fully factual. The hard task is to tease out which bits are historical and which not.
But we also have the simple fact of the church. Though you can argue about the historicity of the gospels it is unarguable that the church did consist of people who claimed to have known Jesus and that they passed on their memories and their faith in him to others. In the church we have an ongoing community rooted in the past which descends from those who claimed to have walked, talked and lived with Jesus. These people, the earliest Christians, claimed that their lives had been transformed by the encounter and they developed an intense commitment that was tested unto martyrdom in some cases. All this for a merely fictional figure!
The Jesus deniers have against them the weight of the consensus of the ancient world, not all of whom believed in Jesus, but none denied his reality.