I would like to emphasize a point you made.
"China has the world's largest navy — what now for the US?"
While that may be true, they are severely outdated. Many from the cold war. Because of this, 90% of their navy is obsolete compared to the U.S Fleet. Keep in mind, we have 19 super carriers, with 10 more being developed as we speak, while China can't field a single carrier besides the Type 001A which has proven to be:
A - Obsolete compared to Ford Class or Nimitz Class Carriers
B - To expensive for China
C - Lack of experienced Aircraft Pilots.
For these 3 reasons, they can't even field their own carrier. The Chinese navy can kiss Air Supremacy goodbye. Most of their fleet consists of frigates, but if they were to go against a CSG, they'd be destroyed without even getting in 50 miles of them due to the Aircraft Carrier the US has.
Now you may argue Submarines, however, once again, America takes the cake. While the Chinese has a little bit more subs, they are old and LOUD. Making them easy to detect and for American Destroyers to destroy. America has state-of-the-art submarines that even the best chinese destroyers wouldn't be able to detect them until far to late.
While they have their Frigates and Patrol Boats, we have our Destroyers, Super Carriers, etc.