The best known very early one is the Old Babylonian Enuma elish, probably dating to the 18th century BCE or so. We don't have any Sumerian version of it, though other Sumerian cosmogonies survive (but they are later). The Enuma elish is very well known because the theogony it describes is structurally similar to several other ones, including the Hurro-Hittite Kumarbi cycle, the Ugaritic Baal cycle, a Phoenician cosmogony attributed to Sanchouniathon, and various Greek Theogonies.

But the Enuma elish isn't the earliest cosmogonic text we have: that position goes to a couple of Egyptian texts that refer to Atum's creation of the cosmos. The earliest versions date to the 23rd century BCE, and survive as dedicatory inscriptions in the pyramids of Merenre I and Pepi II. A copy of the original text can be found in K. Sethe, Die altägyptischen Pyramidentexten (1910), §1652-1656; a translation can be found in J. B. Pritchard, Ancient Near Eastern Texts Relating to the Old Testament (3rd ed. 1969), pp. 3-4.

Edit. As I said, the 23rd century texts only allude to the creation story. For a fuller version, you have to look ahead to the Book of the Dead. There are also several other Egyptian creation narratives.

Some Australian Aboriginal Dreamtime myths date back 10,000 years. The Dreamtime is the period when the ancestors created the world - all of it, and the various parts of it.

On page 29 of 'The Dyirbal Language of North Queensland, Volume 9', By Robert M. W. Dixon (sorry, couldn't work out how to link directly to the page itself), there's a description of a myth which explains how three lakes in the local region were formed:

the camping-place began to change, the earth under the camp roaring like thunder. The wind started to blow down, as if a cyclone were coming. The camping-place began to twist and crack. While this was happening there was in the sky a red cloud, of a hue never seen before. The people tried to run from side to side but were swallowed by a crack which opened in the ground...

Modern researchers took this to be a plausible description of a volcanic eruption. When they checked the geology of those three lakes, they found that they were indeed created by volcanic eruptions - about 10,000 years ago.

It's worth noting here that the Aboriginal people of Australia had no written language: all their history and myths are passed down orally.

There was another myth in the same area about an early ancestor who walked to the local islands to name their local features. Again, the last time the sea level was low enough for those islands to be connected to the mainland was about 8,000 - 10,000 years ago.

Further to this, I watched a television documentary recently which, among other things, showed other evidence of Aboriginal Dreamtime myths which had been passed down for around 10,000 years.

I believe these Dreamtime myths pre-date most other creation myths around the world.

I think the Hindu creation myths may be a potential candidate although I am unsure of the age and there are so many of them. My favorite is the Hymn of Creation in the Rig Veda. Now the Rig Veda is a collection of hymns that has been dated to be written over a period of time between 1700-1100 BC.

Here are a few Hindu creation myths