Well, Egyptian writing ‘proper’ seems to have developed gradually from proto-writing over the course of the 4th millennium BC, so in a sense we have as good an idea as can likely be well-defined. We don’t have the very earliest ‘fully written’ records (and we’d never be able to prove they were first if we could even clarify what that meant) but we do have some bounds… and since the writing system seems to have gradually expanded to encompass the whole language, it’s fuzzy in reality in any case.

EDIT: I suppose one could argue that the moment Egyptian developed the monoliterals, it was technically a full writing system. Not sure how we’d ever possibly know exactly when that was, though.