While China would attempt to send the US out of its backyard by shocking the US with an invasion of Taiwan, that motive in itself would not be enough to push China to war. Beijing believes that controlling more territory is the solution to current problems with its own territory. In urban terms, it would be like believing the reason you have problems in your home is because you don't own the home nextdoor—you deserve to own it, after all; so take it, "by force if necessary." That part of Chinese culture—needing to occupy more surroundings in order to solve problems at home, rather than after solving problems at home—is the part of the Beijing mindset that will actually push China to invade. The time of the invasion will come when Beijing believes that solving its problems at home—specifically with Western press and free speech—can wait no longer. Then, China will invade Taiwan while genuinely believing that all of China's problems within its current borders will thus vanish over night.
But, the US doesn't think the way Beijing thinks the US thinks. While many Americans will be surprised by China's invasion of Taiwan, Beijing will be surprised even more by the American electorate's response to support recompense against China.
In Chinese media, a Chinese Air Force colonel's recommendation that PLA Navy ships ram US Navy ships is not an actual recommendation for strategy as much as it is an attempt at repulsive rhetoric. Chinese culture presumes that a public suggestion is an indirect warning with no intention of follow-through, and because it has no intention of follow-through, it is therefore a "powerful-polite" way of attempting to tell the US to leave. That is how cultural, indirect communication with the Chinese works. Though it is possible that the Chinese might become enraged enough to follow this action by ramming US ships at sea, it would take less rage for China to decide to invade Taiwan. From Beijing's view, unlike retaking the well-deserved Taiwan, ramming a US ship would be an actual assault. If the Chinese-American war begins with a rammed ship, that would indicate a very angry China.