Well, China can create a sporting body with countries that are not aligned with US. Finding the initiative is upto China.
China needs to first establish successful spectator sports domestically then go for alternate sporting bodies. It should start with football and basketball where there already have been massive investments. Invest in grassroots programs, create a culture rather than splurging big on foreign players (which happened in CSL, thank goodness it stopped). It will take a decade or so but will produce results.
Once domestically these sports succeed then it will become financially sustainable and powerful . After that China can easily create new sporting bodies or even dominate the current ones.
Like if i take example of Cricket. Its primarily played by 8 nations. But before India was economically relevant , the cricket body ICC (International Cricket Council) was dominated by Australia & England. India soon became a big market and its domestic league (IPL) succeeded. India became a financial powerhouse in the sport and now BCCI (Indian Cricket Body ) dominates ICC . Aus England monopoly got finished.
Even in US there's MLS. Now 2 decades ago it was considered a joke. With crap attendance and shit quality of play and poor viewership. 20 years later the attendance has grown manyfold, sponsors have arrived and some clubs (LA, AU) are worth more than some European powerhouses like AC Milan, Inter, Atelitico etc. MLS is now on course to surpass Baseball as Americas 3rd biggest sport. Its also projected to surpass German and Italian football leagues in terms of revenue and attendance by 2030.
This growth also helped America become powerful in FIFA and now you have them hosting the World Cup in 2026.
Make the sport strong domestically & then dominate the sporting bodies or create a new one.