The New Testament and The History of the Jews were written in tandem in order to passively "support" each-other.

One need only look at how the Deep State "leaked" a fraudulent article to the Washington Post and then used it as pretextual "evidence" in order to get warrants to spy on Trump and his allies in order to see how this was done. The "histories" written by Josephus were written to build on the New Testament with the intent that each could be used to support the other without seeming to overtly do such, just as the New Testament was written in an overly literal manner so that it seems to fulfill allegorical prophecies via literal events even when the methods and claims used in order to do such defy rational logic.

The Flavians and Josephus had decades to "get their story right" between the "time of Christ" and the time when Josephus' books were published. On top of that, Constantine had another three hundred years to tweak those earlier fables into what would become mainstream Christianity.

A lot had transpired by the time Josephus betrayed his countrymen and went about creating empirical propaganda for the Flavians in the closing decades of the first century AD. Josephus wasn't even born until after the historical Christ would have been crucified, and had not begun writing until long after the fall of Jerusalem. As such, it would have been easy for him to get the basic outline of events that had unfolded, and then fill in and embellish whatever the Flavians required him to. Even so, the Flavian fables barely took hold in the first through fourth centuries, and even fell into disuse shortly after the direct lineage of Flavian caesars ended at the close of the first century, until Constantine - some three hundred years later - himself the first Flavian to rule since the first century - decided to suddenly make his forefather's myths the official state religion of the Roman Empire, which had thus given him and his scribes another three hundred years of "history" to "get the story straight".