Sorry. Writing had already been “invented” 5000 years earlier.
FLASH: Earliest Native American Writing Discovered: Smudges on cave roof shown to be smoke signals.
Turning the "signs" into a coherent way of representing spoken languages took a bit longer ~
To a degree Sumerian writing arose out of the need for accountants to keep books.
Most American Indian writings are more recent than Sumerian but not necessarily more recent than a great number of Old World systems.