It’s important to remember that when Buddhism entered China, it did not enter a vacuum. Like Japan, China already had widespread philosophical traditions. By the time Buddhism reached China, sometime during the first century CE, Confucianism and Daoism had become widespread in China. Both had held great influence over Chinese government. And beyond these ideas, traditional Shamanism provided the grounding for Chinese folk religion.
But also like Japan, Chinese religion does not always fit into the widely understood definition of religion in the West. These philosophical traditions were more states of mind and defined how individuals should interact with each other, without also introducing supernatural elements. Being a dedicated practitioner of one philosophical tradition does not mean you cannot practice another. This is especially true of Buddhism and Daoism, which appear made for each other, in some regards.
These two traditions we ripe for syncretism, when two religious traditions begin to overlay each other and merge into one. From a practice perspective, both use meditation to focus the mind, have similar ethics, and promote kindness to others as a principal virtue. The two come together and became Chan Buddhism, which later became Zen in Japan. This is explored in detail by Ray Grigg in The Tao of Zen.
While neither Buddhism nor Daoism accept supernatural explanations at their core, both have often developed them in different contexts. Some Buddhists expect to be reincarnated. Some Daoists adopted Daoism in addition to their folk practices, such as ancestor worship, spirits, and animism. Buddhism is not, prima facie, antithetical to these practices. This environment was ripe for syncretism and the two practices merged, giving birth to Chan and other forms of Mahayana Buddhism.
Because of this, Buddhism was able to permeate Chinese society quickly upon introduction. Of course, Chinese culture also left its mark on Buddhism, but the ability of each to mould the other led to easy spread and influence for Buddhism and its practitioners.