The first records of how to distill alcohol are from the 9th century AD, way after ancient Mesopotamia. There are records of distillation in ancient Mesopotamia but its of things like sea water into pure distilled water. Italy has the first records of distilling wine, which isn't whiskey. You'd more likely get vodka than whiskey from that. The first reference to whiskey is in the The Red Book of Ossory, from Ireland. https://www.stcanicescathedral.ie/red-book-of-ossory/