I understand the general Marxist theory about why class society arose, there was surplus production and that lead to the institution of private property and the rest follows.
All of that makes sense on a high level but what exactly happened on an individual human level? Conceivably those early civilizations could have elected to go for a more equitable and democratic distribution of the surplus value even if the result would probably not be 100% equitable and would result in some poverty due to material constraints at the time. How do you explain the first appearance of private property and class society on an individual level without delving into some evopsych nonsense about evolutionary instincts or whatever?


The primary armament was typically spear, bow/sling and shield. Swords were really expensive and limited to aristocracy.
And also non-state or proto-state societies had absolutely insane levels of mobilization at war. Typically they could sent in the field 20-25% of total population. This is almost every adult man, and some societies (like Scythians) armed women too. The most mobilization-intensive ancient state society (Rome) had peak mobilization level of roughly 6-8% of total population during the Second Punic War, and most of the rest could barely achieve 1-2% (Carthage and Greek poleis could achieve something around 3-4%, although it is more of a guesstimate than hard numbers).
counting or not counting slave population
damn, their harvests must be really powerful to support such levels of mobilization compared to pitiful battles of medieval england.
This is counting the slave population (it actually was a pretty small fraction in most societies, except those powerful enough to have a strong slave influx from war).
The harvests were shitty. This level of mobilization was balanced by being really short-term, which was one of the weaknesses of non-state societies, because when war was long enough, militias of smaller settlements often just left the main army and went home for agricultural work. So even if they managed to beat back the Roman Army, Rome often won just by maintaining the pressure, until non-state armies (if you can apply the term) started dwindling, then forced the battle on favourable conditions.