From: My Mother, although my Father had some small part.
Unless the PLA plan is awful and implemented incompetently, the initial battle of securing the beachheads should be easily won by China. It has too many starting advantages.
1. I'm not convinced that any build up on the mainland disadvantages the offense. Several reason for this view.
(a) No one is going to launch a preemptive strike on the build up locations
(b) There really is no cost to China maintaining an indefinite build up whereas there is a cost to the Taiwanese economy of heightened defense preparedness for an uncertain attack.
(c) The Taiwan Strait is only 130-180 kilometres wide. That distance allows for a night crossing, whose timing is entirely at the discretion of the PLA. American ships based in Japan are not going to reach the Strait before the crossing has been largely completed.
2. No American administration is going to authorise, without Congressional approval, PLAN ships on their side of the Strait. They probably won't do it either if they move onto the Taiwanese side. I don't see Taipei doing it either. Consider their response to the persistent Chinese intrusions into their airspace.
Thus the initial battle of getting a lodgement on Taiwan is practically guaranteed. Next comes the tricky part, whether the island can be largely captured by the PLA. That outcome is largely determined by (a) political considerations and (b) logistics.
I'm not convinced that Taiwan would be politically united 100% in vigorously opposing the PLA. The younger generation yes, but the older generation, business leaders (with their substantial investments on the mainland at risk) and Kuomintang supporters, perhaps more lukewarm. As to the USA any material support to the Taiwanese military would undoubtedly result in a full blown war with China. Anyone brave enough to argue that the entire American political elite believes war with China over Taiwan is worthwhile. At the very least there would be demands that American intervention be conditional on military support from others. Neither South Korea nor Japan are going to help defend Taiwan. Australian forces might be committed but that would be very unpopular. Expect no assistance from India, the Philippines or Vietnam. Nor would NATO intervene on the technicality that it isn't an attack on a NATO member.
As to logistics, I don't believe that Taiwan, by itself can fully seal off the lodgement beaches from Chinese resupply. That requires American full participation. Is a single American carrier group sufficient to interdict the resupply? Assuming of course the political considerations haven't vetoed the intervention.
The best outcome is that the PLA becomes bogged down and are still fighting 3 weeks after landing. That time allows for the concentration of American assets from elsewhere to arrive to the various battle zones which would not just be Taiwan. Accepting that this is a full blown war which will last years and result in American casualties, means the various Chinese weaknesses can be exploited. But that assumes there is the political will to fight. Also that American reliance on technology does not turn into an achilles heel. Everyone confident that Chinese hacking efforts will not disable American drones, or satellites won't be destroyed. How long will the rare earths stockpiles last.
Maybe not direct assistance but India might make their own moves along the border. The Philippines, South Korea, Japan, and Vietnam have their own problems with mainland China as well, not to mention Russia.
Then the wild card of North Korea . . .
Seek peace but keep your gun handy.
I'm not a complete idiot, some parts are missing!
“Illegitemus non carborundum est (“Don’t let the bastards grind you down”).”
― Julia Child