The roots of writing appear to be in the Stone Age. Pre-literate societies have a certain degree of symbology. You can see this with native Australians into the modern period and ancient rock art.
The Winter Count is more in that ballpark, and looks like an independent creation. The first recognised alphabet in the Americas would be runic, but practically every supposed example outside Greenland seems to be controversial. I do believe that Mesoamerican script would have evolved into an alphabet eventually and a number of North American tribes were moving towards a script independently.
The Dongpa symbols look like they have some influence from Chinese characters somewhere down the line (much like some of the North American syllabaries are influenced by the Roman alphabet).
https://en.wikipedia.org/wiki/Winter_count
Or in Asia the Dongba script, which to me looks like a series of cartoon panels:
https://en.wikipedia.org/wiki/Dongba_symbols