Throughout the centuries, because the church was so powerful and autocratic, one could be persecuted for NOT believing that Jesus existed. Basically the idea is that everyone was forced to believe that Jesus existed.
This is a funny type of irony, when you consider that for the first couple hundred years the opposite was true. Nero blamed the burning of Rome on the Christians. They were killed and persecuted in a number of generations. Even today thousands are killed every year for their faith. In many places in the world in the first century, it would have been much easier to pretend as if the whole “Jesus Thing” never happened. That is however, not what the eye witnesses did, because they totally believed that something had happened.