From what we seem to be learning from the Dead Sea Scrolls, much of the Old Testament had been put to scroll, along with parts of what became the first few books of the New Testament.

Of course they weren't called by those names nor were they dated as BC or AD, such definitions being meaningless to most of the world at the time. AFAIR, the nativity story was dated "during the reign of Ceasar Augustus . . . "
Dave