I would think the romans would know if there was a Jesus, that is the point
They might, and they might not. Think about what you are saying. Three hundred years after the Crucifixion is a LONG time in an era when messages were sent on wax tablets and permanent records had to be carved in stone. . . other less important records could be written down on vellum or a papyrus like paper, but the likelyhood of it surviving for any length of time was not good. Any record worth keeping for posterity had to be pretty damn important for the effort to be made. It required lots of man hours to make copies of any record.
Now consider the time span. . . three hundred years. That is similar to trying today to try find the written evidence of an itinerant preacher who wandered around in 1716 in Colonial America's most out-of-the-way settlements whose preaching resulted in the creation of a cult, and who may have come to a bad end in a clash with authorities. Yet WE have written records and a population that was a lot more literate in general, who wrote letters and kept diaries, and even those records are spread far and wide or lost to history. Almost everything that is known about this preacher is only known about the from the teachings of the writings of his followers and what the seventh through ninth generation of them say happened which has been passed down to them in those writings and oral tradition.
In many ways, Constantine made a political decision to center his Empire on Christianity rather that a factual, reason based decision.
Do I think that Jeshua bar Josef called the Christ existed? Absolutely. Do I believe that He was Who He said He was? Also absolutely. If He was not, His church would not have spread, nor would it have grown to be the world encompassing entity that it has become. The original Witnesses were CHANGED by what they experienced from simple men to amazing MEN who changed the world. That was perhaps Jesus' greatest miracle of all. . . to take twelve simple men, and later a larger group, and instill a fire in them, and to send them out into the world and change it in a very short time so that in just 300 years, this "Itenerant preacher" in a remote backwater of the Empire essentially conquered it, and then went on from there to the whole world. That alone is testimony as to WHO HE IS.