China could sink our carriers in a heartbeat if they wanted.
—
Nope. Even with direct fire the US Navy was hard pressed to sink an obsolete CVN. The old CVN used in nuclear weapons test was not sunk either
China **might** be able to get one hit with its Dengfong 21D, but sink one? No way.
On the other hand, perhaps a few dozen container ships could succeed where missiles fail - given the recent track record of Aegis destroyers vs container ships.
We never tried to sink a CVN with nuclear weapons. There has only been 1 CVN that retired and it was CVN65 U.S.S. ENTERPRISE.