They don't have to immediately pull off an invasion. Tomorrow they could begin a draconian blockade, while strategically bombing the island and begin an assassination & disruption campaign by inserting special forces. They can do it (rather inexpensively) on an indefinite basis, as long as they care to. Nobody can stop that and they have zero concern for the humanitarian disaster it would cause, with their eye on the long-term goal. Taiwan wouldn't last very long in that simple and very obvious scenario, it would rapidly degrade their condition. The world (those standing opposed to China's move) would quickly capitulate, understanding full well that the alternative is all out war with China; the UN would be begging for a settlement peace within weeks (which would result in China de facto taking over Taiwan). Mostly all that would happen to China are some sanctions, which China would shrug off (along with some dramatic, harshly worded PR releases). At the end of it, China won't need to invade with a large amphibious assault, it'll enter Taiwan largely unopposed as part of the brokered peace settlement.
China is very rapidly building up its naval capabilities. It will be able to invade Taiwan this decade. That isn't a maybe, it's a certainty.