In late January 2020, China:
* Announced there was human-to-human transmission.
* Completely sealed off Hubei province (population: 60 million).
* Implemented lockdowns in cities throughout China.
Yet most countries did next to nothing for a month or more. It wasn't until hospitals in Lombardy, Italy started filling up that people in Europe and the US started to take the virus seriously. So my prediction: better information from China (which the Chinese government itself did not necessarily have anyways) and more dire warnings from the WHO would have had no effect. Following WHO recommendations would already have been a massive improvement over what European countries and the US did.