Several sources I've read (both Chinese-focused and steppe-focused) have pointed out a dialectic between stable, prosperous Chinese polities and more centralized, more powerful steppe confederations. When China was fragmented into many states during the Zhou period, there were no great powers on the eastern steppe comparable to, say, the Royal Scythians on the Pontic Steppe, the Cimmerians who had plundered the Near East, or the Saka/Massagetae that first fought the Achaemenid Persians and then were incorporated into their army. But shortly after the Qin unification of China, a great steppe empire emerges along the Xiongnu people based in the Ordos region, north of the Qin capital area. This Xiongnu Empire was the first empire of the eastern steppe, and would be followed by various Turkic, Mongolic and Tungusic empires that also formed in the east and eventually migrated westwards.

The broader historical pattern is a feedback loop between states in China and the Eastern Steppe, not only because of warfare but because of economic and political exchanges that could be even more significant. Like the Romans, most Chinese empires beginning with the Western Han tried to influence their "barbarian" neighbors through a mix of subsidies, royal marriages, trade policies, and punitive warfare. But aside from national policy, the existence of a rich, populous single market in North China was a stimulus to nomadic society in and of itself, in the form of both trade and plunder. The emergence of a powerful Xiongnu ruler commanding an elite bureaucracy and disciplined army may also have been influenced by the process of absolutist government reforms in Zhou China that culminated in the Qin-Han unification. In either case, the creation of a unified empire under a powerful central authority happened in both North China and the Eastern Steppe almost simultaneously and afterwards there is a close correlation between the economic and political health of the two regions. In short, the Eastern Steppe tended to produce large nomadic empires with sophisticated military and political structures because of the constant interplay between themselves and the Chinese empires.

But besides the question of why major steppe groups emerged in the East rather than in the West, we also need to explain why they later migrated westwards. There is a complex set of factors that fed into this. I would argue that, because of their Han-Xiongnu political heritage, the eastern steppe groups (including Avars, Turks, Uighurs, and Mongols) had organizational and tactical skills that gave them an advantage over the original Iranic nomad groups in the western and central steppes. We also have to recognize internal politics- civil wars, the splitting of clans, or a group seceding from the confederation- could all trigger migrations out of the eastern steppe, whether into China or westward to Central Asia. Once in Central Asia, the economic pull of India, Iran and the Black Sea could continue pulling them westward even as pressure from further migrations built in the east, pushing them onwards.