Earlier quoted context omitted.
Writing has been independently invented two to four times that we know of in the last five millennia. (Some scholars debate whether cuneiform, Egyptian hieroglyphs, and Chinese writing were all independently invented, with Mesoamerican writing being the other almost indisputably independent invention.) Anatomically modern humans date back at least 200,000 years and probably would be capable of inventing writing long…
The Egyptian and the Sumerian culture were very strongly linked with near identical cultic symbols and building plans for temples up until 3100BC. Chinese writing came suddenly over 1000 years later (minus some shamanic symbols), connectable via the Anu seal (which of course is tentative and will be denied by Chinese nationalist)
There was prehistoric (i.e. pre-writing) trade between Sumer and Egypt. Scholars have argued that the idea of writing based on the rebus principle—but not a specific writing system—may have been communicated one way or another through this trade contact.
Your claim that the cultures were "very strongly linked with near identical cultic symbols and building plans for temples" is a new one for me—and I volunteer at a museum of ancient near eastern archeology. The material culture of pre-Dynastic Egypt and Sumer are rather distinct from each other. And when we do get writing describing their religion, those are also rather distinct from each other.
