The Chinese can afford to bide their time, for now. The US is otherwise engaged, in fighting a foe that the Chinese have little affinity for, and unlikely to ever form an alliance with. This also provides the Chinese with considerable cover for their own military preparations, partly in the event that Western nations ever waver in their will to contain and domesticate the Islamic nations, and partly to be ready to use threat of force to cow a weakened Western alliance. Right now, threats to overrun Taiwan are coached in rather timid diplomatic language, because the US still answers strongly and forthrightly. But should the will of this country ever wane, the "one-China" policy will become a reality, and Taiwan will become another Hong Kong. And since the "overseas Chinese" are placed in so many other countries, there will be further claim to extend the hegemony of Chinese rule.
This places them in direct confrontation with the more amorphous Islamic influence that extends across most of southwestern and southeastern Asia. Only one obstacle stands in their way - the subcontinent of India, neither Chinese nor Muslim, the world's largest democracy, as they like to describe themselves, and a growing economic giant in their own right.
All Europe's dreams for the end to US influence to the world would soon be realized. Pretty empty victory, of course, because Europe itself will be almost unrecognizable within a few decades.
One of the things in our advantage. Is the fact that we are at "war". And the only way to be good at it is to do it. We are developing alot of skills in doing our battles.