Ehhhh...Whiskey Pete isn't wrong but he's still wrong.
If the US Carrier fleet lined up on the back side of Taiwan, dropped anchor and didn't move for as long as it took for the Chinese to find them, fire their missiles, and the Americans did nothing in the 10 minutes between launch and impact, including not bringing the Arleigh Burke's with the Aegis systems....well yeah.
In reality though, the carriers are constantly moving around in a protective bubble defended by a few missile cruisers, a few destroyers, frigates and subs,..... and a full compliment of F 35's among other treats. Finding them is harder than you'd think (ocean is mad big yo) and getting a targeting solution on one is again, harder than just finding one. Then you need the American missile defence cruisers to not shoot your shit down, which given how successful an older, lesser system has been in shooting down Russian hypersonics in Ukraine...
So like, realistically...yeah China could sink a carrier but probably only if an American carrier was really close to Taiwan (like, as in they decided that they needed to use F-35's using only internal fuel to protect Taiwan so need to be within 100-150km of Taiwan) so China got to use their bigger, better land based hypersonic kit on them. If a carrier is fucking about 1000+km from the Chinese coast, just doing random carrier shit in SEA, I don't see it.
This sounds like the thing people at the Pentagon say when they're about to ask for funding on a new weapons programs.