Well, I’m talking about two different things here, the first being the hypothetical date for Jesus’s birth.
A close reading of the events points to 4 BC as being the year, and the time of year being sometime in Spring “when shepherds watch over their flocks by night.”
As for if Jesus was real at all… well, there’s absolutely no contemporaneous evidence from his lifetime that he was ever real, no written record, no first hand account, nothing.
The first mention of Jesus was by Flavius Josephus around 93-94 AD, some 60 years after the Crucifixion, but even that may be a 3rd century insert by a Christian transcriber known as Eusebius of Caesarea.
The problem with the Josephus text is two fold: 1) We don’t have the original, just copies of copies of copies. 2) None of the works quoting Josephus prior to Eusebius make any mention of the Jesus quote which makes it highly suspicious.
The bulk of the New Testament isn’t a result of Jesus at all, it’s all because of Paul, formerly known as Saul of Tarsus.
Saul had his own thing going on, which wasn’t entirely popular, then he claimed to have this amazing conversion experience on the road to Damascus, changed his name to Paul, and started talking about this Jesus fellow.
We know Paul existed, we have his letters, other writings, and peers talking about him. How odd none of that exists for Jesus…
A couple of really good books to read about Saul/Paul and the early days: