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

[The Mikado]

If you are hellbent on using Josephus to prove Jesus's existence,  the smart play is to sidestep the Testimonium Flaviam entirely and instead invoke the reference in Book 20, Chapter 9:

Festus was now dead, and Albinus was but upon the road; so he assembled the sanhedrim of judges, and brought before them the brother of Jesus, who was called Christ, whose name was James, and some others, [or, some of his companions]; and when he had formed an accusation against them as breakers of the law, he delivered them to be stoned:

Given Josephus' career, it's quite likely he was literally there when James was executed, too. If not, he definitely would've known people present.

It also fits in that James, as the head of the Jerusalem Church, would have a significantly bigger following 30 years after Jesus' execution than Jesus himself ever had while living, and his execution would've been really noteworthy as the head of a very troublesome faction.

[The Mikado]

The point is that crucifixion was not a punishment for blasphemy or anything the Jewish priesthood would have cared about convicting Jesus for.

The point I was making was that the Gospels make clear that Roman law prohibited the Jewish priesthood from putting anyone to death. Furthermore, some commentaries have indicated that both the trials before the Sanhedrin and Pilate were outside Jewish and Roman law - an important point to note that under the laws of man, the crucifixion was not justified.

Of course, a non-Roman citizen had no right to appeal or anything under Roman law.

It's why St. Paul, who WAS a Roman citizen, had such a complicated execution story and survived way longer than he otherwise would have.

(Arrested in Jerusalem in ~57... I want to take my case to the Emperor! ... Finally sent to Rome in ~60... Nero's incredibly busy and Paul gets to spend literal years in Rome doing his thing before Nero gets around to hearing his appeal and having him killed in ~64)