Not the first instance of warfare, which surely predates recorded history, but of an organized war between civilizations. For the purposes of this question I'll define a war as:
- Defined scope: the war had a beginning, and end, and specific belligerents. Not an ongoing state of hostility between people groups.
- Dedicated fighting force: the war was fought by a military of some kind, rather than armed commoners who skirmished when they happened to meet.
- State-driven: Military action was enacted by one or more governments. (One state campaigning against disorganized tribes would count.)
The earliest war I can find a description of is Sargon's conquest of Sumer at the Battle of Ur in c. 2271 BC, which led to the establishment of the Akkadian Empire. I suspect there were earlier documented conflicts in Sumer or other very early agricultural civilizations.