I am a bit confused. A former Protestant High School History teacher explained the existence of Jesus as, "We believe that Jesus Christ existed during the reign of Octavian."
My atheist History college professor today explained, "Jesus Christ did exist in Palestine during the reign of Octavian."
The word believe could be interpreted as trust in good faith. With the word did, there would be no doubt in the existence of Jesus Christ.
I would appreciate anyone to not cite Wikipedia and/or biblical scriptures on this. Please don't hold back. I won't take offence from any response since I'm an atheist.
For whatever consensus is worth, the consensus among historians working in relevant fields (Ancient History, New Testament, Classics) is that Jesus existed. At a basic level, before anyone goes making claims about who this Jesus was or what he did or taught, there is a fundamental agreement that on all current evidence and the balance of historical research, that yes such a figure existed.
The claim that such a figure never existed at all is generally labelled Christ Mythicism. The only almost-respectable figure to promote the theory is Richard Carrier who at least holds a PhD in a relevant field. However he is largely considered a fringe theorist.
For more discussion on Jesus as a historical figure, I suggest you consult the faq. I am only answering your question about consensus opinion in the scholarly community.