How do we know that prehistoric hunter-gatherer societies were egalitarian?

It doesn't help that the question contains a no true Scotsman type equivocation (most, relatively). This is, however, common to Wikipedia's coverage.

It also doesn't help that the comparison of social stratification between gather-hunter societies and, for example, late capitalism produces tautologies. Gatherers didn't wage-enslave the majority of the planet to the expanded reproduction of the value form.*1 Even gatherer societies, with differential production relations (class), cannot martial either the agricultural output or the down season labour*2 of early monument building class societies. Even amongst oppressed labouring class gatherers, the only social egality broken by different relations to creating wealth is gender. In a monumental society architects, master masons, and carpenters lack the egality of herdspeople, or field labourers.

To a large extent the question is answered through gathering producing no (or weak) ruling classes, and no specialist labouring occupations.

The equivocations being: gerontocracy; chiefs; priests, shaman, and magicians; and, of course the gendered social relations. Relative to heavily classed societies these are minimal variations—even compared to semi-autonomous highland agricultural communities with rigorous land egality cultures.

Notes

*1 the value form being capital and thus simultaneously wage labour and the commodity. We would recognise it as wage labour societies where labourers have no effective control over how production is organised, where commodities are produced for sale on the market, and where profit or Soviet-style growth whip firms into the pursuit of profit or growth.

*2 flood agriculture and agriculture in general involve periods where the work required is higher or lower. The period of lower work on crops is the down season. This is when a society can corvee or martial labourers to work on other projects like monuments.

The claim that prehistoric hunter gatherers were egalitarian is mostly supported by:

• analogy to some modern or historic hunter-gatherer societies
• lack of monumental buildings in the archeological record
• same for elaborate graves
• hunter-gatherers can only possess as much as they can carry so little chance to amass possessions.

A recent example for this argumentation would be Yuval Noah Harari's Brief History of Mankind.

Anthropologist David Greaber that bullet points 2 & 3 are not quite true and some prehistoric hunter-gatherer bands were not egalitarian:

...there is the undisputed existence of rich burials, extending back in time to the depths of the Ice Age. Some of these, such as the 25,000-year-old graves from Sungir, east of Moscow, have been known for many decades and are justly famous. ... dug into the permafrost beneath the Palaeolithic settlement at Sungir was the grave of a middle-aged man buried, as Fernández-Armesto observes, with ‘stunning signs of honor: bracelets of polished mammoth-ivory, a diadem or cap of fox’s teeth, and nearly 3,000 laboriously carved and polished ivory beads’. And a few feet away, in an identical grave, ‘lay two children, of about 10 and 13 years respectively, adorned with comparable grave-gifts – including, in the case of the elder, some 5,000 beads as fine as the adult’s (although slightly smaller) and a massive lance carved from ivory’.

Similar sites exist in the Dordogne or Basque country. However, comparable burial sites are far and wide between. The same goes for paleolithic monumental buildings.

So it appears that the claim "prehistoric hunter gatherer societies were egalitarian" is, strictly speaking wrong, or only true most of the time, in most places. It was certainly possible for very early societies to develop complex stratifications and engage in huge projects, like Gökpeli Tepe or Stonehenge. On the other hand, large more or less temporary cities existed (where wildlife was abundant enough) even pre the neolithic revolution, and some show no sign of strong social hierarchies.

So the evidence is less clear and everything is more complex and fascinating than commonly assumed.