I’m always struck by Luke 3.1, 2: Luke firmly fixes John the Baptist’s appearance in history:

• In the fifteenth year of the reign of Tiberius Caesar, 
• Pontius Pilate being governor of Judea, and 
• Herod being tetrarch of Galilee, and 
• his brother Philip tetrarch of the region of Ituraea and Trachonitis, and 
• Lysanias tetrarch of Abilene, 
• during the high priesthood of Annas and Caiaphas, 
• the word of God came to John the son of Zechariah in the wilderness. (Luke 3.1, 2, ESV, bulleted for clarity)

Peter’s testimony is clear:

For we did not follow cleverly devised myths when we made known to you the power and coming of our Lord Jesus Christ, but we were eyewitnesses of his majesty. For when he received honor and glory from God the Father, and the voice was borne to him by the Majestic Glory, “This is my beloved Son, with whom I am well pleased,” we ourselves heard this very voice borne from heaven, for we were with him on the holy mountain. And we have the prophetic word more fully confirmed, to which you will do well to pay attention as to a lamp shining in a dark place, until the day dawns and the morning star rises in your hearts. (1 Peter 1.16 – 19, ESV)

And John echoes the theme: this stuff really happened!

That which was from the beginning, which we have heard, which we have seen with our eyes, which we looked upon and have touched with our hands, concerning the word of life—the life was made manifest, and we have seen it, and testify to it and proclaim to you the eternal life, which was with the Father and was made manifest to us—that which we have seen and heard we proclaim also to you, so that you too may have fellowship with us; and indeed our fellowship is with the Father and with his Son Jesus Christ. And we are writing these things so that our joy may be complete. (1 John 1.1 – 4, ESV, emphasis mine)