I’d pick an event we have no concrete knowledge about, or we have conflicting accounts of and we’re unsure what exactly happened. Some candidates:

• Death of Bartia, brother of Cambyses II - was Darius the Great lying about there being an imposter of Bartia? (probably)
• Sack of Babylon by Mursili I, but with some astronomical dooblydoo to be able to precisely date it. Maybe a better way would be to pick an early eclipse before the Hittite sack of Babylon and ask some locals who the king is.
• The writing/dictation/whatever of “The Exaltation of Inanna”. Was it really by created by Enheduanna? Was it a bit of legend or royal propaganda?