You put a lot of faith in the Chinese military, which hasn't fought a major war in over 30 years. It failed to win against Vietnam 30+ years ago or against the US 70+ years ago. Neither has it been able to retake Taiwan for over half a century.
Going back to what you said....it'll be obvious if/when China moves it's missile launchers. Taiwan has a robust defense around the island which can intercept most, if not all, Chinese missiles.
If China sends "hundreds" of missiles then so will Taiwan.
Taiwan has missiles that can reach up to 600 km and is working on missiles that can reach up to 2,000 km practically able to hit anywhere in Eastern China.
Example:
View attachment 19345
It also has the Patriot ABM system, which has destroyed multiple Russian hypersonic cruise missiles so far, as well as home grown ABM systems with a range of 300 km.
They're also building more ABM sites. They also have loitering munitions that have a range of 1,000km and can fly for up to 100 hours, at a speed of 185 km/hr.
I really wouldn't underestimate Taiwan and overestimate China.
China recently said that it doesn't care if it losses 100-600M people in a war with Taiwan. You can clearly see through this "statement" that they expect to lose millions, if not hundreds of millions, of people.