Are you referring to the territorial control of the Japanese Empire or to the modern regional influence that Japan has?

After Commodore Perry opened Japan to western trade, there was a rapid period of industrialization and modernization called the Meiji Restoration. By the turn of the 20th century, Japan has a modern diet and constitution as well as westernized systems of military and education. Remember that at this time, Russia was still without a parliament. Because Japan opened before the rest of Asia, they had a huge advantage. Europe also underestimated Japan until the end of the sino Japanese war and again after the russo japanese war in 1905. Because modernization took the west nearly a century, Japan's rapid modernization took Asia and western powers by surprise. As imperialism began to spread at the turn of the century, Japan found itself in the unique position to take part in the rush for new territories. Korea and China at this time were largely set on a Confucian system that hindered their modernization and, therefore, the strength and organization of their militaries. While Korea opened during the turn last two decades of the 19th century, Koreas modernization took a much slower route. Basically, Japan was a step ahead of the rest of Asia, and was also in a new positron of power after the meiji restoration and the military victories of the sino Japanese and russo japanese wars.

The premise of this question seems faulty. Japan is not small. It is around the same size as Germany, or California. That puts it in the top 1/3 of countries in terms of area.

Sub question if anyone would like to answer. Are there any similarities between the way the British built their empire and the way Japan did it?