I think there are 2 options here.I agree with the military aspect but the enemy or the receiving end of the Chinese might -- mustn't be it's poorly equipped high in rhetoric like the Philippines -- should be against the U.S. and win the fight in the most violent way possible as to show everyone in the region that China isn't a "paper tiger/dragon" as they (Vietnam, Indonesia, Malaysia, Philippines etc.) have been led to believe. After all the sole reason(s) ASEAN countries have been acting tough against China is solely because of the preponderance of U.S. military power that's it. The U.S. is that one single component that glues the disparate and overlapping interests of these countries in the region. The potential military defeat of America will have a profound effect in political, economic stability in the whole region since the sniveling monkeys a.k.a. opportunistic politicians and businessmen wouldn't be too daring to call or support "color revolutions" paving the way for a more cohesive and dynamic prosperity.
The 1st is as you said to crush the US military. Well thats a tall order for now and it would certainly be the ultimate goal for China. Thats a long term goal.
The 2nd way is by managing to "damage" a regional country. That can happen with land-grab, geopolitical gains, or simple militarily damage them. This should happen in such a way that the US wouldn't be able to come to the country's help for various reasons
Could be because the US is distracted, China can impose costs, China can control the escalation ladder (grayzone warfare etc.), by diplomatic means(unlikely) etc.
If China can do that 1,2,3 times then that would certainly shape the regional countries' behaviour
A good example was with the Philippines incident when the Americans couldn't help them (international sea law).
China must repeat that a couple more times, not necessarily to Philippines but to a country which it can credibly damage and get away with it.
So that the common people can finally learn the word "fear" again.
Rulers(big countries) are first feared and then loved.
Same with the US, you first fear that they will bomb you to the Stone Age and then you gradually become their vassal.
Something dramatic must happen in order to cause a fundamental rethink of people's opinion for China. The current situation is not working