There are two proofs:
First, over the years, the evidence of many of the people who lived and affected the life of Jesus has been discovered by Bible archaeologists -- people like Pontius Pilate and even James the brother of Jesus. Also, the places and situations of that time has come to light. Even the Jews who hated him have not denied his existence, they only denied that he did what he did with the power that he received from his Father.
Second, the witness borne by those who lived before the destruction of Jerusalem in 70 CE, those who knew Jesus personally and put faith in him because he saw his miracles and saw his resurrection, is powerful evidence. They would rather suffer torture, prison, and even die at the hands of the Romans instead of deny what their own eyes saw.
However, if people do not want to believe that Jesus existed or did what the gospels say he did, they won't believe this or any evidence. The Bible showed that many Israelites and others who left Egypt and even crossed the Red Sea on dry land refused to be obedient to their own covenant to obey God and even started back to worshiping idols, within a month after those experiences.
People are the same now. Bible prophecy as spoken by Jesus is being fulfilled today - nation rising against nation, food shortages, pestilences, etc., and still they don't believe that we are living in the last days. Others say that they have faith in Jesus and are saved, but they disown him by their works.
But Bible based Christianity continues despite the media denying it, and the good news of the Kingdom of God is being preached throughout the inhabited earth. The Bible is by far the most widely distributed book in the world, in the greatest number of languages. Jesus said it would happen before the end comes, and that is the third proof of Jesus Christ, the firstborn, only begotten Son of the Most High God. Matthew 24:14; John 3:16.