Looking across Chinese history, the officials in every dynasty were really from established aristocratic families. Even the so-called top scholars from poor backgrounds were often just clever children from down-and-out branches of prominent clans. In ancient times, if an ordinary person with little education wanted to rise and become an official, joining the military was probably a decent path. When war broke out, if you crawled out of a pile of corpses and earned merit, you might be granted some rank or post—but most people were just cannon fodder. Most people in ancient China simply toiled away, working all 365 days of the year without rest.
Now look at today. Things are actually far better than in ancient times. At least in terms of probability, the odds of a poor person climbing the social ladder through their own efforts are far greater in modern society than in ancient times. Of course, various forms of invisible hereditary privilege still exist, and it is very hard to eliminate them completely at the root, but compared with feudal society, things are already much fairer.
Directly comparing ancient and modern times along a single vertical axis has limited persuasive power. If you really want to argue that "the probability of class mobility has increased," you could first look for verifiable reference points—for example, the number of civil service exam admissions relative to population, or contemporary data on years of education and occupational mobility—and then define the comparison period and region. Otherwise, it amounts to nothing more than a personal impression and can hardly support a judgment like "the best."