Josephus is definitely credible, but I don’t think the name Cuzar/Kozar/Khazar shows up in his works. The rise of the Khazar kingdom would also have been ahead of his time. However, that name does show up as the son of Togarmah, the grandson of Japheth, in documents dating from the Middle Ages and shortly afterwards.
Three steps we can take, using experience and intuition, which help to understand that the established historical record is likely to be significantly falsified:
1. observe and acknowledge that deceptiveness is inherent to human communications, including in the historical record
2. understand the strength of motivation for the elites to falsify the historical record
3. recognize that revelations in our age of the degree and frequency of deception by authorities regarding current events can be extrapolated to illustrate the extent of deception dating back many centuries