Greater China already produces more chips than US, even more than rest of the world combined, the challenge is design. To be more specific, it's fabless and architecture, in the global commercial sector (excluding military or other state sectors).
Tech reserves are abundant, see supercomputers, however status quo in the global commercial sector on fabless/architecture is not even a tech challenge, but a business one. China needs to place strategic investments across the whole value chain from hardware to software, setting industry standard and build ecosystem. For example, China just missed the opportunity to acquire ARM (now owned by Softbank), Chinese firms must find other ways, organic or M&A, to cut into fabless/architecture. The advantage is, like TD-CDMA is influencing global 5G stadard, China does have a huge home market (and industrial complex), if not world's biggest, to influence global standard-setting.