Sorry, there seems to be a disconnect. Jesus was buried in a cave, right? Jesus dies before Constantine, right? Show that a man named Jesus was buried at this location.
Ok. I found an article which begins like this and goes some way to answering your question. The link is at the bottom and you will have to scroll down that page to see the rest of this article about proof that it might be the burial place of Jesus.
http://news.nationalgeographic.com/2016/10/jesus-christ-tomb-burial-church-holy-sepulchre/
WAS THIS REALLY THE TOMB OF CHRIST?
While it is archaeologically impossible to say that the tomb recently uncovered in the Church of the Holy Sepulchre is the burial site of an individual Jew known as Jesus of Nazareth, there is indirect evidence to suggest that the identification of the site by representatives of the Roman emperor Constantine some 300 years later may be a reasonable one.