Josephus was long dead by the time xtianity really got going in the mid 2d century.
Prior to that we have only the ecclesiastical lies put forward by later church writers to justify themselves and hints of gnostic groups or other splinter cults worshiping some "christ-figure" but generally flying below the radar with the notable exception of Pliny the Younger's report from Asia Minor....which fails to mention "jesus," "crucifixion." "mary," "joseph," "pilate" or "jerusalem" among other failings.
Prior to that we have only the ecclesiastical lies put forward by later church writers to justify themselves and hints of gnostic groups or other splinter cults worshiping some "christ-figure" but generally flying below the radar with the notable exception of Pliny the Younger's report from Asia Minor....which fails to mention "jesus," "crucifixion." "mary," "joseph," "pilate" or "jerusalem" among other failings.