Just as the US has satellites to keep track of the PLAN, China has plenty of satellites to keep an eye on the USN too:
If the USN fleet is positioned 400 miles away from China, it'd be hopeless to think any PLAN surface ships could move toward it without being spotted.
The obvious choice would be to send an air strike and use air-launched anti-ship missiles. No missile defense system is perfect. If you can shoot enough missiles at it, sooner or later you'd score a hit.
In such case the question would be, how well can the PLAAF perform against the F-18's, can enough JH-7A or other strike aircraft get within missile launch range, how many strike aircraft can you send, and what are the anti-ship missile's guidance system, performance, and range.
Under ideal conditions, you'd have PLAAF fighters enage the carrier aircraft, and have your strike aircraft launch long-range "fire and forget" anti-ship missiles in large numbers, then run back to base. i.e. if each JH-7A can carry 4 anti-ship missiles, a squadron of 15 planes = 60 anti-ship missiles.