You've touched on a problem that the linked answers from u/Antiquarianism and u/Philitian address: https://www.reddit.com/r/AskHistorians/comments/b8j08h/how_much_evidence_do_we_require_to_say_a/

Sumer, Egypt, all those ancient civilizations didn't emerge from a vacuum. There were large settlements, sedentary agricultural populations etc before. This gets into what is a "civilization." There's a textbook definition that is commonly used that requires, most notably, writing, and a socially stratified urban environment. A now-deleted user talks a bit about the history of that definition here, and its issues: https://www.reddit.com/r/AskHistorians/comments/1w9yxf/what_is_the_working_definition_of_civilization/

By that definition, particularly the writing example, Sumer is first. But that's a very specific definition. u/mcKinnon42 has some archaeological insight here: https://www.reddit.com/r/AskHistorians/comments/b5yrmi/how_certain_are_we_that_the_first_civilizations/

In terms of are we missing something, probably not, but I think it's a question of definition. They list a few large neolithic sites, like Göbekli Tepe, Jericho, Talianki, and Çatalhöyük. Why aren't these civilizations? When you think of the word civilization and whatever criteria you think is important, they very well may be.