The Testimonium Flavianum was an later insertion. None of the 2nd century apologists who cite Josephus mention it, though it would have greatly helped their case. Josephus wrote that people were mad at Herod for killing John the Baptist. Some 3rd or 4th century church father, such as Eusebius, noted the glaring omission and added the ill-fitting blurb about Jesus.
The gospel of John was more likely written around or even after 120.
The gospel of John was more likely written around or even after 120.