Yes, Flavius Josephus lived during the same period as Jesus of Nazareth. Josephus was born around 37 AD and died around 100 AD, while Jesus is believed to have been born around 4 BC and crucified around 30-36 AD. This means that Josephus was alive during the lifetime of Jesus and even wrote about the events surrounding early Christianity.
Josephus was a Jewish historian and his works, particularly ‘Antiquities of the Jews’, include references to Jesus, John the Baptist, and the early Christians. His writings provide valuable insights into the historical context of the time, although they are not without controversy regarding their authenticity and the degree of embellishment.