Not sure if cave paintings qualify(20000BC Europe), but my straight off the top of my head answer would be Sumerian Cuneiform(4000-3500bc). Well at least of the stuff they have found or admitted they found
Representational art does not count as writing. Writing has to be representation of words themselves, not objects or creatures they refer to. I agree with your assessment of Sumerian as the first true writing that we know of. However, the transition from drawing to logograms was gradual so those Sumerian samples are probably just the oldest surviving ones we've found. If we could find something 300 years older it might show a continuum between drawing and writing, with no clear transition point.
