No, the burden of proof is on the people who assert the existence of giant omnipotent deities that no one can see save (apparently) on grilled cheese sandwiches.
If you're going to talk about 'historical records', well, there are literally hundreds, even thousands of fictional stories that could well pass for historical records, in most cases much better even than the Bible. For example, take Charles Dickens's A Tale of Two Cities. I could claim that it is a historically accurate record, in novelized form, of the actions of a number of real people during the time of the French Revolution. You would probably have a difficult time showing my claim to be wrong, save that it just happens to be common knowledge that A Tale of Two Cities is a work of fiction, first written many years after the French Revolution. By comparison, the Bible is much EASIER to demonstrate as wrong, since it claims a number of things that go against known scientific facts: That the Earth was created 6000 years ago, that insects have four legs, that there was a guy who could make bread and fish out of nowhere, and that the Cheops Pyramid was submerged under eight kilometers of water for five months. Yet you believe the Bible (or at least, parts of it, including parts making claims about magic and invisible deities) to be fact, and reject A Tale of Two Cities as fiction. Why?