All nations adopt something from their neighbors. Japan is relatively isolated so the only nearby long-lived civilized realms were Korea and China. Hence by default these became the main foreign influences on ancient Japan and they have had a lot of time to influence the Japanese. Sometimes rulers try to stem the flow of foreign ideas, but that's only a temporary blip in the process as in time more open-minded rulers will come to power. Let's not forget that governments often deliberately copy some of the practices of successful nations, hoping it will make their own nation richer and stronger. Since China has been such a dominant power in East Asia it's only natural the higher social classes in Japan would look more to China than Korea (and Korea is of course also heavily influenced by China). As a populous empire China produced a lot of cultural products (everything from goods to stories) that the rich would have loved to consume. Once the higher classes adopt new practices and fashions, they will influence commoners too.

tl;dr geography and time made Chinese influence inevitable.

China during its imperial days was the strongest civilization in East Asia. Its vast land and resources allowed to remain dominant in projecting power to its neighbors.

The attitude towards the Chinese emperor was that it was under the mandate of heaven, and that China was the center of the world. All non-Chinese were regarded as barbarians. The neighboring countries of course were treated with better respect if they acknowledged what China was and adopted Chinese culture as a way of civilizing itself. In that way, China would see the countries more as tributary states than barbaric lands. China did not acknowledge that there were other civilized places, even calling the Europeans that they interacted with as barbarians. China saw her culture the culture of the world.

Obviously, when Japan industrialized and became far more powerful than China, it no longer saw China as country in which to follow. It saw China fail miserably under Western empires and thus began copying the West rather than China.

Source: On China, by Henry Kissinger