We humans have records, of a sort, of the conflict that led to the establishment of a unified Egyptian monarchy under a king known to us as Narmer, an event we date to 2950 BCE. We can say that there were three main habitation sites in Upper Egypt around this time (walled cities) and scholars of the subject can trace the ups and downs of each, from evidence of trade, burials, and heirarchic organization. There's even a rock tableau showing the ruler of one of these towns, Tjeni (presumed to be an ancestor of Narmer) winning a battle. The size of city walls, and a notable number of cranial injuries among the dead, also support the idea that this was a period of military conflict. After subduing his rivals Narmer commissioned a ceremonial palette, showing him smiting enemies with a mace, to celebrate his success; it was discovered buried in mud in 1898. While there are no written narratives, this aggregation of archeological evidence is certainly enough to identify a non-mythological period of warfare, ending with the establishment of the first true Egyptian monarchy. See generally Wilkinson, The Rise and Fall of Ancient Egypt, Random House, 2010.
(My personal favorite isn't anywhere near as old, but in the British Museum Assyrian rooms there's a wall frieze showing a military campaign of about 900 BCE in great detail, from the seige of a city to the victor's (Ashirnasirpal II) triumph. A mighty victory, but for the fact that the name of the place the Assyrians were at war with is illegible.)
After reading this question, I decided to do some digging. I'd like to talk briefly about four battles -- which may or may not have occurred -- and 1 which likely did: the Battle of Mingtiao, the Battle of Banquan, and the Battle of Zhuolu. These battles occurred around circa 1600 BCE, 2500 BCE, and 2500 BCE, respectively.
The problem with early battles and wars is that much of their events are shrouded in legend and mythology.
** The Battle of Banquan (~2500 BCE): **
According to Sima Qian in his history of China from about 2594 BCE to 97 BCE (finished in 94 BCE), this was the first war in Chinese history. It was fought between the Yellow Emperor and the Flame Emperor (I recognize how ridiculous these names seem.) It is unknown how many soldiers fought. However, according to records, the soldiers were trained for war and the goal was to consolidate the surrounding tribes.
According to records, the Yellow Emperor's success led to the battle of Zhuolu between the Yanhuang tribes (led by the Yellow Emperor) and the Jiuli tribes (led by Chiyou.) Chiyou had become jealous of the Yellow Emperor's success and attempted to invade. In mythology, there was extensive use of magic, giants and evil spirits. However, given that magic, giants and evil spirits do not actually exist, this part is considered mythology. Should the battle have actually occurred, there was likely a deep fog and the deployment of technology (Yellow Emperor used a fancy contraption that always pointed south -- an early compass), resulting in a loss by Chiyou.
**Battle of Mingtiao: **
It has long been disputed whether or not the Xia Dynasty actually existed (most say that it is legendary.) However, it is known that the Shang Dynasty did exist. The Battle of Mingtiao is a disputed battle that ended the Xia Dynasty and marked the beginning of the Shang Dynasty. It is unknown how many soldiers the Xia generals would have had under their command, however, it is unlikely that the Shang generals would have had more than 4-5k soldiers under their command. The reason why this battle is important (even if it never actually happened) is because it establishes the idea of a noble revolution.
EDIT: 2500 BCE, not 25000 BCE...