^ The first divisions of the Japanese navy arrive at Busan on April 13, 1592, spearheading the invasion
INTRODUCTION
When Japanese daimyo Toyotomi Hideyoshi, successor to Oda Nobunaga, invaded the Joseon Kingdom of Korea in 1592, he set his sights on much loftier goals in his near future. The Korean Peninsula was merely the stepping stone towards a much greater prize: the Ming Empire of China. Unlike the previous Japanese invasions of Korea in the 7th century AD that were meant to bolster their Baekje ally against the Silla Kingdom (which eventually unified the peninsula), this time around the Japanese intended a broad conquest of the entire region and beyond. The ruins of Japanese castles built in Korea from this decade speak volumes about their ambitious resolve to expand, colonize, and establish an East Asian empire. The Japanese succeeded in driving Joseon forces all the way to the Yalu River on more than one occasion, repelled by joint Ming-Joseon counterattacks. Allied forces were of course aided enormously by the repeated defeats suffered by the Japanese navy at sea against the Joseon Admiral Yi Sun-sin.
KOREA: CHINA'S USEFUL BUFFER STATE
The question must be asked, though: was Hideyoshi's larger goal an entirely realistic one? Ancient Han China succeeded in expanding its realm into northern Vietnam and northern Korea by the 2nd century BC, but that was long before those regions were developed and part of larger kingdoms that posed huge stumbling blocks for mainland expansion. Case in point: the Chinese Sui Dynasty's disastrous failed invasions of the Goguryeo Kingdom of Korea at the end of the 6th century AD and the Tang Dynasty failing half a century later to hold northern Korea against Silla (who was previously a staunch ally and later reestablished as a tributary vassal). In the 16th century, Joseon Korea, again a vassal state of the Chinese empire, served well as a buffer between China and Japan. Before this, the only significant mainland attempt to conquer Japan had been Yuan emperor Kublai Khan's two failed naval invasions in 1274 and 1281, both launched from Korea (which by that point was conquered by the Mongols, with the Goryeo Kingdom on life support as an occupied vassal). It is difficult, therefore, with the handful of major conflicts to assume Japan couldn't be conquered by China or vice versa.
LOGISTICS, STUMBLING BLOCKS, MONGOLS AND MANCHUS
If some of you here are convinced that Japan could have conquered China, let's talk about the numbers then! Specifically the troops available to Japan under Toyotomi Hideyoshi and if they could be used to garrison everything he had in mind. Given the rebellious conditions in Korea, it is tough to say that, had he controlled every square inch of Korea and then launched a proper invasion into China through Manchuria or across the Yellow Sea, his new Korean subjects wouldn't start revolts that would frustrate such grandiose plans. Aside from these matters, there are also the Mongols and Manchus to consider. Hideyoshi's invasions came a decade after the death of Altan Khan, the Mongolian ruler who had led several successful forays deep into Ming territory. The Northern Yuan Dynasty (a remnant of the fallen Yuan Dynasty of aforementioned Mongol emperor Kublai Khan), led at this point by Buyan Sechen Khan, nominally ruled all the Mongols. However, this was far from the truth. Despite being fractured, the Mongols could have posed a serious stumbling block to the Japanese if they had made it as far as northern China. With chaos all around, it would have been the perfect situation for the Mongols to move in and plunder once more. The Manchus would perhaps have posed an even greater threat in this regard. It was at this time that Nurhaci (predecessor to Huang Taiji, ruler of the Northern Jin Dynasty and founder of the Qing Dynasty) was busy unifying the Jurchen tribes of Manchuria that would later become the Manchu in 1635. With the Momoyama Japanese vying with the Ming for control of northern China, the Jurchen tribes under Nurhaci's banners could have seen some profit in taking advantage of the turmoil, perhaps even conquering Liaoning province long before 1626.
EUROPEAN PRESENCE IN THE AGE OF SAIL
Also, what role if any would the Dutch, English, Spanish, and Portuguese have played in this effort? In the 1590s they were trading heavily with Japan and seeing only limited trade with Ming China at a handful of ports (by now Macau was already well established as a Portuguese trade colony). The Italian Jesuit Matteo Ricci had already been living in China for a decade when the war broke out, but was only accepted at the imperial court in Beijing in 1598, when the war was concluded. It was only after the war that he became the leading European figure and astronomer at the court of the Wanli Emperor, creating world maps, dictionaries, and translating works such as the ancient Greek mathematical treatise Euclid's Elements into Chinese. If the Japanese had successfully invaded northern China during the 1590s, would this have encouraged European powers to press for greater trade rights further up China's coast and even into the interior (that would be hypothetically controlled by the Japanese)? Would the Jesuit presence in China have been even more enhanced by a Japanese occupation? Or would the Protestant powers have gained the upper hand (seeing how Englishman William Adams became a trusted figure over the Spaniards at Tokugawa Ieyasu's court)?