That might be six days, after the PLA manages to land a full division, and ALL of it's logistic support on the island. If you think that won't require the deaths of many thousands of lives beforehand, then I'd suggest you rethink it.
So that could be six days after the first week. The Taiwanese aren't going to make it easy. They aren't just going to surrender without a fight. They are already dug in, in hardened bunker complexes, that are probably designed to withstand nuclear strikes- because they have had to cope with the threat of of Chinese nukes pointed at the island for decades. China can't hope to keep such an operation a secret, given the logistic footprint involved, so it's likely that the world will be well aware of a PRC invasion of Taiwan at least a week before it takes place. So basically, that adds a week to the time the US will have to respond, and the time that Taiwan will have to prepare. Given that Taiwan holds both the tactical, and moral highground, has the advantage of American INTEL, will be fighting on their own turf from prepared defeses, and is armed to the teeth for a nation of that size- I think the PRC is either headed for a rude awakening, or will have to nuke the island...
Two- to three weeks time. That's about how much time it would take for two full ESG's based at Washington, and California to reach the theater. And lets not forget that Taiwan has other allies in the region besides the US- to include nations such as Japan, Australia/New Zealand, Thailand and South Korea. All of the above have very modern, and capable naval and air forces. They are not likely going to sit idly by, and allow the PRC to bulldoze Taiwan- particularly when the US is also involved. And then there will be the outrage at the UN....
Frankly, that's just too long, given that the US military has assets RIGHT there in the theater, and can position at least two full ESGs
on the situation in less than two weeks. Not to mention a handfull of SSN's, the US Air Force at Okinawa, Japan, Guam, Hawaii, Alaska, the continental US, and whatever else may be transiting to, or from the IO/PG.
In my opinion, China must seek to appease Taiwan, in order to achieve reunification in a diplomatic, peaceful manner- or they are going to have to destroy the entire island, and everyone on it. Choosing the latter may just mean the end of China, and the rest of world- when one takes into account all of the nuclear weapons the participants are pointing at one another.