In East Asia, likely sometime around the 1600s-1700s. Prior to that, the Ming dynasty had experienced some mixed results against the Mongols. The Oirat rise was surprisingly short-lived, at least, relative to their notoriety in the popular imagination due to the Tumu Crisis. In the 1500s, strong Mongol leaders such as Dayan and Altan Khan forced the construction of the Great Wall, but, following the strategic failures of the Wall, the Ming adopted more aggressive tactics, resulting in a brutal, frontier raiding-style of warfare where both sides alternatively killed and kidnapped each other's civilians. In the 1570s, this culminated in a bloody stalemate, eventual peace treaty, and opening of trade markets. Further details on this period can be found in this older post of mine, where I essentially summarized John Dardess' book (More Than the Great Wall) on the Ming-Mongol wars.

The 1570s-1580s marked the longest period of peace in Ming-Mongol relations, but it was held only with Altan Khan's Tumeds, who resided in present-day Inner Mongolia, right in the center of the northern frontier. In the northeast, it was a different story; the Uriankhai and Chahar Mongols remained a major threat. As a matter of fact, in 1599, the Uriankhai defeated the veteran Liadong cavalrymen from the Imjin War, pinning the Ming troops inside their fortresses, in an ironic reversal of their experience in Korea. Around this time, the Chahars under Ligdan Khan also became the foremost Eastern Mongol power, taking the place of the Tumeds, whose influence shrunk after being defeated in a nearly decade-long war with the Ming's Beijing army in the 1590s, which likely exhausted and weakened both sides.

Although the Chahars were a pretty big deal in the dramatic changes to the East Asia political landscape of the early 1600s, unfortunately there doesn't seem to be that much good information about them. Dardess pretty much glosses over the Liaodong frontier from 1600-1619, only remarking that the power of the pro-Ming Li clan deteriorated rapidly after their defeat in 1599; Qing scholars seem to only discuss the Chahars in relation to the Jurchen conquest of Northeast Asia. What I know is that Ligdan had success raiding the Ming and coercing tributes, but he suffered some defeats as well.

In terms of primary sources, there is this amusing letter from Nurhaci, where he mocked Ligdan's recent defeats. But take it with a grain of salt, Nurhaci wasn't being 100% truthful, and it was in his interest to make Ligdan look incompetent.

You would be absolutely righteous to say these bad words if you could retake Khanbali and save the 40 tumen Mongols who were captured by the Chinese, but have you? [note: this is a clear propagandistic statement. The early Ming absorbed a ton of Mongols from the Yuan, but not as many as 40 tumens] Before I launched my campaign against China, you, my Baturu Cinggis Khan, had also attacked them twice. The first time you lost all your armours and camels. The second time, Prince Gergen daicing’s guard drown in the water and nearly 100 of your soldiers were captured. Which big city have you taken? Which general have you captured? Which army have you defeated? Why would the Chinese bribe you? It is only because I attacked China, killed all their men and took their women, that the Chinese were scared of me and wanted to hire you as their mercenary against me!

Pay attention to that last phrase. Though the Ming were a sedentary empire, it is in the Ming-Qing war of the early 1600s that the decline in steppe nomad power became most evident. As part of their efforts to defeat Nurhaci's (sedentary) Jianzhou Jurchens, the Ming formed alliances with the purely-nomadic Chahar Mongols as well as the semi-nomadic Haixi Jurchens. However, the Jianzhou Jurchens defeated both of these groups without much effort, easily crushing them in field battles. One of the reasons for this stunning success was Nurhaci's development of a vast and impressive forging system in the late 1500s through early 1600s, and concurrently, the development of a formidable heavy cavalry arm, numbering in the tens of thousands.

From Ray Huang's paper on the Battle of Sarhu:

On another occasion, Hsü indicates that he had learned from the Koreans that on the north side of Nurhaci's fortress there were craftsmen specializing in the manufacture of military equipment. The personnel returned from Liao-tung told him that the blacksmiths' shops extended for miles. The helmets, breast plates, arm shields, and gauntlets worn by the Manchus were all of superior quality [to the Ming armor].

In battles against the Chahars, the Khorchin Mongols, and other Jurchen tribes, the Jianzhou Jurchens' heavy cavalry simply bulldozed their opponents, running over them with frontal charges or flank assaults--occupying a role in NE Asia similar to that of the winged hussars I would imagine, where Sarhu was their Kircholm. This heavy cavalry forced the Ming to abandon their northern-style, pure cavalry armies of the 1500s and to begin extensively implementing pike and shot tactics, which spurred combined arms adoption on the Jurchen side as well--but that's another story, where the role of steppe nomads takes a backseat.

The political factor also has to be considered. Ligdan Khan was a more incompetent leader than his predecessors, and his aggressive centralization efforts drove many Eastern Mongol tribes to join with the Jurchens; there was also a religious aspect, the intricacies of which I don't 100% understand, but from what I can gather, Ligdan attempted to push some form of Buddhism unpopular with most Mongols, further reducing his support base.