In the deepest archaeological levels of cities in Mesopotamia, and in the lowest levels of ancient temples, such as of that Eridu, archaeologists have uncovered material remains of a culture they've named "Ubaidian," for Tel al'Ubaid, near the city of Ur. Included in these was a distinctive pottery that worked its way around much of ancient Mesopotamia so thoroughly it's often used as an indication of an Ubaid "horizon." The tel was first investigated by H. R Hall around 1920. Later in the decade, when C. Leonard Woolley uncovered the royal graves at Ur, he found some of the greenish-clay pottery Hall had found at the tel, though these pieces were far outshone by the spectacular grave goods from Ur.
The Ubaid culture is generally assigned the time period 5000-4000 BCE. It is not known who the Ubaidians were, nor what language they spoke, as they have left no written record. Woolley thought they may have been a Semitic people and pointed out that in later times, wave after wave of semi-nomadic Semites worked their way into Mesopotamia, either peacefully or by force of arms. Woolley thought they were original Semite settlers, who were then invaded by the Sumerians. The origin of the Sumerians themselves is still unknown, but because their language was an agglutinative one, which Samuel Noah Kramer sees as bearing some resemblance to Ural-Altaic languages, it has been thought that they came from Central Asia, perhaps from around the Caspian Sea.
There is a common reference to the Ubaidians being the first civilization. The Ubaidians had migrated to the Tigris-Euphrates river valley (alluvial plain) from the steppes of northern Mesopotamia (Assyria) c. 4600-4800 BCE. Their adaptation of irrigation led to enough food production to support a larger population and their farming villages led to small cities, with natural boundaries creating city/states. The practice of religion and forays into warfare supported the appointment of priests and warrior chieftains which ruled the city/states. The creation of other trades beside farming and organized religion led to the consensus that this was civilization. However, further excavations at tel Halaf predate the Ubaidians so who knows? Archaeological study of the near east is a relatively new development for that area, and new finds rewrite their history repeatedly. Also, it is considered that the Egyptians were the first civilization.
There is quite a bit known about the Sumerian civilization. People known as Ubaidians in the fifth millennium formed settlements that would become Sumer. The Sumarians after 3250 BC began to intermarry with locals and thus formed Sumerians. The Sumerians would eventually form the Semites, those people living in the Middle East and Mesopotamia. They had a long history of decline and prospering, and built cities discussed in the Old Testament.