There are historical records of somebody named Jesus that lived at the time.
No, there are no contemporary primary sources about him from his purported lifetime. All sources stems from several decades to centuries after his purported death.
The consensus about his existence is established based on the likelihood of him existing, but his existence can never be verified with absolute certainty. And what he actually did or said is impossible to determine as well. On that we can only rely on what people living relatively long after his purported death wanted him to have said.
No, there are no contemporary primary sources about him from his purported lifetime. All sources stems from several decades to centuries after his purported death.
The consensus about his existence is established based on the likelihood of him existing, but his existence can never be verified with absolute certainty. And what he actually did or said is impossible to determine as well. On that we can only rely on what people living relatively long after his purported death wanted him to have said.