Can Antiquities of the Jews be proof of Jesus existence and divinity

[Okay, maybe Mike Johnson is a competent parliamentarian.]

You really can't "prove" much of anything about non-royalty from the first century, but most historians consider Josephus one among several documentary sources for Jesus' existence, yes. It's difficult to overstate how fringe mythicism is these days. Getting from there to His divinity, on the other hand, is several steps further than historical methods can or should take us, especially since parts of the passage are almost certainly later interpolations.

[Okay, maybe Mike Johnson is a competent parliamentarian.]

Pontius Pilate was recalled back to Rome due to his brutality in Judea. 

Which is why I LOL at people who blame Jooz for Jeebus' execution and believe all that nonsense in the Holy Buybull. 

As is often the case when you post about this, there's a great point buried underneath your signature posting style. Historical-critical scholars are almost universally of the belief that Pilate was much more bent on executing Jesus than the Bible suggests and that the Gospels stressing the culpability of the Jewish leadership instead was a writerly choice with political and strategic dimensions to it.