What “first” can and cannot mean
The title makes a claim that is common in popular books, and the honest answer is that it depends on what is counted. Mesopotamia has strong claims to several important firsts, but the idea of one single “first civilization” is difficult to defend. Scholars disagree on what a civilization is, and the definition used (cities, writing, monuments, states, social inequality) changes the answer. Dating is also uncertain at the edges, with overlaps of a few centuries that radiocarbon dating cannot always resolve.
A cautious summary is that southern Mesopotamia was among the earliest places where large cities and writing appeared, and that Egypt developed early writing and a unified state at around the same time. Several other regions followed independently.
The well supported Mesopotamian firsts
Early cities. In the Uruk period, in the fourth millennium BCE, the city of Uruk grew to cover a large area and contained monumental buildings, workshops and administrative buildings. Estimates of its population are uncertain, but it was very large for its time. Surveys of southern Mesopotamia suggest a strong shift of people from villages into a few large centres during this era, which is why the Uruk period is often given as the best known example of early urban life. The Sumerian urban life that followed in the Early Dynastic period is far better documented.
Writing in a recognised form. The oldest tablets with proto-cuneiform signs, found at Uruk, date to about 3300 to 3000 BCE. Most record quantities of goods and rations, not stories. Over the following centuries the signs came to represent sounds as well as ideas, which allowed them to write language. The later cuneiform writing system was used across the Near East.
Early bureaucracy and administration. Seals, counting tokens, sealed clay envelopes and numerical tablets show a society keeping detailed accounts for temple estates. The sexagesimal number system developed here is still reflected in how time and angles are measured.
Where the claim becomes debated
Egypt. Egyptian writing appears at a very similar date. Inscribed labels from a tomb at Abydos are dated to around 3300 BCE, and some scholars have asked whether Egyptian writing was inspired by Mesopotamian example or developed independently. The evidence does not settle the question, and many scholars favour independent development with some contact. Egypt’s unification under a single ruler, around 3100 BCE or somewhat later, produced a very different kind of state from the Mesopotamian city-states. Egyptian hieroglyphic script and cuneiform solved the problem of writing differently.
The Indus. The Indus Valley cities, such as Harappa and Mohenjo-Daro, reached their mature form around 2600 BCE, later than Uruk. They are distinctive in having planned streets and drainage, and they traded with Mesopotamia, which called the region Meluhha according to many scholars. The Indus script has not been deciphered, so some questions about its society remain open. The earliest Indus settlements and farming communities go back much earlier than the cities.
Other regions. The Norte Chico region of Peru shows monumental architecture around 3000 BCE, and China’s early states came somewhat later. In the Americas, cities arose entirely independently. There is no evidence that any of these developed through contact with Mesopotamia.
Before the cities
Calling any one place “first” also hides the long background of earlier achievements. Farming and village life began in the Near East thousands of years before Uruk. Monumental construction predates cities, as shown by the Gobekli Tepe monuments in southeastern Turkey, which were built by people who, as far as is known, did not farm. Southern Mesopotamia built on a long record of earlier settlement, including the Ubaid villages, and some elements, such as the sail, the wheel and irrigation, developed over a long time across several regions.
A more useful way to put it
Rather than a single winner, historians increasingly describe several early centres, each of which developed in its own way. Mesopotamia’s special importance is documentary. It left a large written record, much of it on durable clay, which lets us see how an early urban society actually functioned. It is therefore more accurate to say that Mesopotamia produced some of the earliest cities and the best documented early states, than to say it was the first civilization of the world.