I'd be interested to know who you claim those atheist archaeologists and historians are.
The older versions of the gospels describe Pontius Pilate as a procutrator--modern versions have corrected that egregious error, pretending it had never been made. Prior to a ruling by Claudius, sometime after 40 CE, procurators were not more than imperial accountants--they did not govern administrative units.
The Pilate stone shows that he was a prefect. As such, he would not have commanded no Roman soldiers. At the time the gospels were written, they weren't yet doing that "Jews as Christ killers" bullshit yet, because so many of the cult were Jews. They were trying to make the Romans the villians of the piece. But a prefect would only have had two thousand or so auxilliaries
, not Roman soldiers--you know, local boys. His brieff was to protect the land trade routes which lead to the sea. He had no reason to keep any of his troops in Jerusalem. In fact, Jerusalem was not the capital of anything at that time. The "ca;ital" of the Prefecture of Iudaea was Caesarea Maritima, well to the north of present day Tel Aviv. There was no reason for Pilate to have been in Jerusalem. Certainly not for a religious observation of a subject people. In fact, according to Flavius Josephus, Pilate was contemptuous of local customs and religion. He was recalled to Rome for attacking a Samaritan religious procession.
Pilate was not going to be taking any **** from Ciaphas. The Prefect appointed the High Priest from a short list provided by the priests of the Temple, so that Roman authority could be sure the job was held by someone they approved of. He sure as hell wasn't going to listen to the crowd about what to do with a prisoner--no Roman official ever listened to the mob, not if he wanted to keep his job. As a prefect, he had no authority to condemn or execute anyone. If he had wanted to do that, he'd have been obliged to send the accused off to the governor of Syria.
I'm just getting warmed up, but you can have more later, it you want it.