Strategypage is a good source and their take on China's ability to invade Taiwan is interesting:
On paper China ought to be capable of quickly conquering Taiwan. The reality is different. Chinese military analysts often discuss openly the problems and risks of such an attack. The current Chinese strategy towards Taiwan is more threat than reality but that threat is backed by a lot of ballistic missiles, more than Taiwan can intercept.
... The basic Chinese strategy appears to be the immediate use of over a thousand ballistic and cruise missiles ... to be used to try and cripple Taiwanese air force and navy, as well as attacking headquarters and communications targets. Almost simultaneously, China would try to invade with airborne and amphibious forces. Without those missiles, Taiwan's air and naval forces would make it very difficult, if not impossible, for the invasion force to cross the straits. Military analysts have examined various targeting strategies, and defensive moves the Taiwanese could take. In most cases, the Chinese succeed. The barrage of missiles can do serious damage to Taiwanese air and naval forces, giving Chinese air and naval forces an opportunity to get ground forces ashore. If Taiwan keeps improving its defenses, China remains unenthusiastic about attempting an invasion. [emphasis added]
So 1) China can't invade and conquer Taiwan quickly; 2) But China can put ground forces on Taiwan; and 3) Yet China is unenthusiastic about invading as long as Taiwan keeps arming up.
So China can seriously damage Taiwan's air and naval forces, which would clear the way to land troops; and China's lack of enthusiasm--not lack of capability--for invading is dependent on Taiwan continuing to build their military capabilities to match the Chinese improvements.
And consider that if China's rulers feel they need a foreign victory over a core interest to rally an unhappy population, lack of enthusiasm is no longer a factor deterring an order to invade.
So yes, China can invade Taiwan. Maybe they lose. Maybe they win. Heck, maybe it's a stalemate, which wouldn't turn out well for Taiwan in the long run.
Note that America isn't a factor in that balancing act. That's because I believe China would try to conquer Taiwan before America can decide to intervene and reach the area in force through Chinese A2/AD forces.
