Can you explain what your definition of civilization is?

My definition of civilization pretty much revolves around the development of urban centers that demonstrate a level of human cooperation in groups larger than their evolutionary tribal size (something like 150 individuals). In that sense Sumer was certainly one of the first civilizations that fits this description. Because of the erratic flood plane weather that the Mesopotamian region experiences the management of levies was critical not only to the survival of the individual farmer, but to his neighbors as well. Thus arose a need for cooperation. This type of cooperation honestly probably dates even further back than the Sumerians, but because of the advent of cuneiform came during the lifespan of the Sumerian civilization, we actually have some information aside from archaeology about Sumerian civilization.

Much of answering this question is dependent on what you define as civilized, and it is unclear if the Indus River Valley civilization developed its urban centers earlier than the ones created in Mesopotamia. The Indus River Valley civilization had the cities of Harappa and Mohenjo-daro which I find to be the most fascinating and advanced ancient urban centers. These cities had working sewers, public baths, and were enormously organized. My understanding is that the two civilizations developed independent of each other which is also really interesting, although I'm pretty sure they traded with each other eventually. The Indus River Valley was much more forgiving climatically so I don't think they developed the same level of irrigation and flood plane control that the Mesopotamian civilizations had. Anyway, the Mesopotamian civilizations and the Indus River Valley civilization are sometimes crudely described as the genesis of the Western and Eastern world respectively.