Well, it'll be almost impossible to even start in the current environment, seeing how quickly the likes of mainstream western media labels any media to do with China being state funded. CGTN would be an example where everything they post is plastered with a big banner on YouTube/Twitter stating Chinese government affiliation.China really needs this and they need to build this sooner rather than later. It takes time to build institutions, raise media profile, attract talent, and raise public perception and trust in these vectors of propagandistic and diplomatic warfare. Fortunately, the Chinese government is quite frankly in one of the best positions to construct such an apparatus. With the finances and pull it has, it can bribe or negotiate with the likes of google to put Chinese-sourced articles and resources at the top. The PRC can leverage so many instruments to construct this new facet of international power.
When people in the west try to hear from experts on American strategy, finances, or institutions, they'll find American and western experts and government mouthpieces in media and on the internet. When people in the west want to hear the same thing about China, they hear from American and western experts instead. Forget not being trusted. China, honestly, doesn't even seem to want to speak for itself. This is something that, quite frankly, will cost Chinese lives if reunification goes hot.
Unless those main streams of western media consumption gets replaced by an alternative they will always have a headstart against any attempts to convince them otherwise. Ultimately media response is dependent on political messaging and currently the West sees China as a bigger threat then even Russia itself.