How about China expanding south and west, taking Nepal, India and Afganistan?
That would do it.
Two words: (The) Great Game.
The only time that China could have expanded into the areas you mentioned was during the Qing dynasty, because the only other dynasty to control Tibet politically was the Yuan. The Tang would be the next closest possibility, but they overexpanded themselves to some extent after taking Central Asia, as shown in the An Shi Rebellion. If it was hard to militarily control areas outside of China proper, I highly doubt they could have expanded even into Tibet, especially because the latter was also a powerful state that conflicted with the Tang over Central Asia, and even sacked Chang'an. The Yuan already had issues with the other Khaganates, so expanding to the west and south could have made matters worse for the dynasty.
China regarded India as a source for Buddhism, so it would be extremely hard to make the Tang even attempt to invade any of the Indian states, not to mention the geography in the Himalayas. The Qing probably could not have expanded any further because they conflicted with Russia to the north, Britain was influencing Tibet from India, and France attempted to open settlements in southern China from Indochina. It could have expanded in the 1700s before the tensions existed, but it had already overexpanded itself, and were unable to take Burma, so I think it would be highly unlikely.
A USNA would be the only one that could really compete. Potentially if the Portuguese grabbed the River Plate, you could get an uber-Brazil including Argentina, Uruguay and Paraguay. Fourth largest possibility is to have China hold Mongolia, and to take Korea and Vietnam.
In line with the above, I'm not sure how China could hold all of the areas you mentioned at the same time unless you can come up with a significant butterfly before 500. Because the northern nomads were able to use horses efficiently, the Han never completely absorbed the Xiongnu, the Tang never politically absorbed the Gokturks, although some joined the Chinese in certain expeditions, and the Ming was unable to conquer the Northern Yuan, which caused them to rebuild the Great Wall. The Qing did control Mongolia directly, but you would need to butterfly away Russian influence significantly to prevent Mongolian independence, or make sure that the Nationalists reunify China after World War II. The PRC did not invade Mongolia because they viewed it as a political ally.
The last time that China invaded Korea, it took 70 years to conquer the peninsula. Goguryeo fell mostly because it was politically unstable, and Silla allied with the Tang. One of the reasons that the Sui fell was because they spent four costly campaigns trying to vanquish the state, and it took three more by the Tang to finally accomplish their objectives. However, Silla quickly retook control of most of the peninsula, and Balhae was established 30 years after Goguryeo fell, eventually going on to reclaim most of Goguryeo's former territory. The Mongols invaded Goryeo for 40 years, and ultimately decided to grant it autonomy with a compulsory military alliance under the Yuan. Joseon was established because its founder pledged to retain close links with the Ming, and the latter came to Korea's aid when Japan invaded it. Vietnam was a Chinese province until around 900, but it only consisted of the area around Hanoi, and I highly doubt that any of the Chinese dynasties would take the trouble to invade Champa when it was a loyal tributary when they had more pressing issues, not to mention the Khmer Empire.
In other words, Russia is able to retain its size mostly because most of its territory consists of Siberia, which means that it is sparsely populated. In order to have a state which is of comparable size, you would need to find a large region that was barely populated to begin with, and almost no competition from other countries. The latter is probably why North and South America could not have hosted such a large country, not to mention geographic conditions.