There were cultures whenever humans got to the point of teaching things from one generation to the next, I suppose. In terms of what are usually termed 'civilizations', that is a culture with "writing" of some sort and some form of urban organization, the first would be the early Mesopotamian cities in the Middle East, in what is today the Gulf of Persia. "Mesopotamia" is Greek for "land between the rivers," specifically the Tigris and Euphrates. These cities are properly termed the "Uruk culture," named for Uruk (or Erech), their earliest known capital city. These cities began about 6000 BC, in what are today the countries of Iraq and Iran.
The area did not receive much rainfall, but was watered in the east by the two rivers. By cutting vegetation and building up swampy areas the earliest farmers, a people known as Ubaidians, created more fertile soil. These people, originally from the Caucases, built the first cities of the world, in the lower part of the plain, called Babylon. Later they intermarried with newcomers called Sumerians. Babylon was divided in two, Akkad in the north and Sumer in the delta to the south. These cities included Babel, Ur, Lagash, Nippur, and eventually Ninevah and many others.
The Sumerian language is unrelated to any other known toungue. Akkadian, a Semitic language which became the lingua franca of the Sumerian world, is the language many early records are written in, including the most complete copy of the epic of Gilgamesh. Their cuneiform or "triangle-shape" form of writing remained standard for two millenia, even though alphabetic writing existed well before 1800 BC.
The earliest historic document, or earliest record made of a contemporary event, was found in 'Obeid, just west of Ur, in 1923. It is a three by four inch marble slab laid in a cornerstone of a temple, inscribed "Annipadda, king of Ur, son of Messanipadda, has built this for his lady Nin-Kharsag," she being a mother-goddess.