That the aristocrats would be willing to follow a warlord, and later emperor, from peasant origins is the more surprising aspect from a western perspective. Was there less emphasis on superior birth in China compared to Europe?
The short answer is yes, hereditary rank or status played a much smaller role in imperial Chinese society than it did in the West. The formal hereditary aristocracy in China mostly disintegrated over the course of the Eastern Zhou through a mix of partible inheritance (which led to large numbers of "noblemen" who economically were effectively commoners), bureaucratic expansion (which allowed the central government to better manage lands and people, cutting out the nobility's middleman role in taxation), and escalating warfare (killing off or dispossessing the biggest lords). Later Chinese elites were defined by wealth, education, and social connections but hereditary principles were not strongly entrenched.
The longer answer is that there were various points in Chinese history where some form of hereditary social class reemerged (whether elite or servile), but they were temporary and fragmentary. For example, during the Age of Disunion between the Han and Sui, sons of officials were entitled to an official position of their own based off of the highest rank their father achieved, and a class of serf-like retainers existed under the major landowners. The Yuan and Ming both based their armies on hereditary military households of low status. But generally, a mix of meritocratic ideology and the state's centralizing tendencies eventually broke up any truly hereditary social group that developed.