In Chapter 12 of Guns, Germs, and Steel, Jared Diamond discusses the invention of writing. He mentions that it was invented independently in a small number of places (Mesopotamia, Mesoamerica, China, and Egypt) and spread either directly (as in cases of conquest) or through a process of idea diffusion, i.e., people coming into contact with societies that had writing and either adapting writing systems or creating their own in response.
There are two major reasons why other societies did not develop writing independently or at an early period. The first has to do with practicality. Even if a hunter-gatherer or nomadic society encountered the idea of writing, a mobile society would not be able to carry around an archive of documents even if they wished to do so. Instead, important cultural information was preserved in oral traditional epic, which could be stored in people's minds rather than on physical objects.
Next, only complex settled societies need written records. Land ownership and taxation records, for example, are only needed by large urban societies. Registering births, marriages, and citizenship are only required in large societies because in small tribes, everyone knows who is married to whom, which children were born to which parents, and all the details of kinship networks. Extensive trade and labeling of goods follows on having a significant economic surplus and trading via third parties, something unlikely to be needed by smaller and less settled societies.