I am no historiam or theologist (sp/rightword?) But I did (sleep at a best westrn srry had too) have a very in depth back and forth with some 'historians' and bliblical whathaveyou's.
Now let me preface this by saying I consider myself catholic. (obviously not the best catholic, but I work on do unto others.. thats #1)
But the challenge I put forth was 20 dollars if anyone could prove (preponderance of evidence) that Jesus Christ ever existed. Human, Son of God or otherwise. (That challenge doesn't apply here you guys are a bit smarter than the group I was in, IMHO)...
As you mention Antiquities is a secular book. (straight history no mythos).
The argument they presented was that Jesus was first mentioned in Antiquities book 18 and 20. (around 100 AD).
This is disputed however and wikipedia says that most modern scholars have decided that this mention is most likely a forgery....I find this an over simplification and the truth is shrouded in documents I can hardly interpret if I do speak the language..
Here is a related article.
www.forerunner.com/blog/is-josephus-passage-about-jesus-a-forgery