China is still at least a decade away from being anything more then a regional superpower in military terms. Their navy is still mostly littoral and the term "green water navy" (coastal and ocean near the own nation) was invented more or less to explain what China's current capability is. Their air force is large but lacks long distance bombers and their army is in the transition from a conscript-based foot infantry dominated force into a modern mechanized army. China's neighbors should be very, very scared of the PLA, but it still doesn't have the capability to challenge the USA. If current ratios for both are sustained the PLA will be a contender in the late 2020's or early 2030's and that's assuming that the USA doesn't react and that NATO decides to look the other way if China tries to military challenge the USA.
This is one of those situations when no one can realistically invade China, because their military is just that large. But China can't strike against anyone outside of their immediate home region which prevents them from being a global contender or a serious military threat to the USA or Europe. And even in 2035, the USA will still have twice the number of aircraft carriers that China plans to have and US carriers are decidedly bigger.
I suspect it's not just that but having appropriate alliances. Without a great deal of fleet or other support, an aircraft carrier is mostly just a gigantic target (a criticism that could be made of the Royal Navy - alone it lacks the support ships to adequately defend any aircraft carrier it deployed). For any sort of substantial operations, you'd want a land base. Whether China has these is questionable, so there's plenty of diplomatic work to do, and there would be a lot of resistance.
Also, I fundamentally believe that the only way a country can learn a lot about warfare is by doing it. The USA has regularly carried out operations from which it will have learnt a great deal and constantly refreshed: tactics, experience, ironing out a lot of small equipment problems, logistics problems, weeding out incompetent officers etc. In the Napoleonic wars, it took many of the combatants about five years to catch up with France. In WW2, maybe 2-3 years to catch up with Germany even with constant, intense fighting to learn from.
China has not carried out a meaningful military operation in decades, and even then did so in large part with tactics based on quantity over quality, which are unlikely to be useful far from its borders logistically, so it requires a change in doctrine, too. It's got a long way to go to learn all that. Russia might give it some training and support, but I can't help but feel Russia might be much less sharing than it has been as China increasingly poses it a geopolitical and military threat too.