Supposing there were such documents purporting to have been written by a member or members of the Sanhedrin, and/or Pilate himself, you wouldn't question or doubt the provenance and authenticity of such documents??
Cordially,
Sure I would. We have several verisons of Jospehus. Forgeries are rampant, which is another reason why all historical documents must be taken with a grain of salt. Which is permitted, it seems, except when it comes to the Bible.
Nevertheless, documents that could be corroborated and coming from converted Sanhedrin and Pilate would greatly enhance the Christian story.