You may not be concerned about putting the theory into the generally – accepted ancient Chronology, but I was and it does show that the predynastic Egyptian culture undermines the Babel -theory for how various languages originated.
As for generally accepted theories and dates for origins of written languages, there is none. As I’ve mentioned, there’s two camps – a single origin of all languages and multiple independent origin of languages.
Writing was long thought to have been invented in a single civilization, a theory named “monogenesis”. Scholars believed that all writing originated in ancient Sumer (in Mesopotamia) and spread over the world from there via a process of cultural diffusion. According to this theory, the concept of representing language by written marks, though not necessarily the specifics of how such a system worked, was passed on by traders or merchants traveling between geographical regions.
However, the discovery of the scripts of ancient Mesoamerica, far away from Middle Eastern sources, proved that writing had been invented more than once. Scholars now recognize that writing may have independently developed in at least four ancient civilizations: Mesopotamia (between 3400 and 3100 BCE), Egypt (around 3250 BCE), China (1200 BCE), and lowland areas of Southern Mexico and Guatemala (by 500 BCE).