Strip away media narrative on both sides, an impartial timeline would be:
Wuhan medical community recognized a new pneumonia of unclear cause in late December during winter and the height of influenza season. The novel Corona Virus was identified, WHO was notified, the genome was sequenced. This took roughly 1 week. Then it took 3 more weeks of "stability management" before central government quarantined WuHan and essentially shutdown the entire country right before the most important holiday of the year and the largest annual human migration.
4 weeks for identification to evaluation to 3 months of aggressive techno-authoritarian quarantine, and assuming 2nd wave and import cases can be managed until the vaccine - China just demonstrated the first civilization model in human history to be able to suppress a virus of this magnitude in large countries. Other countries are only recently adopting the war analogy, China executed it on a dime. How they'll fair in rebooting society is unknown.
Was there missteps? Yes. Could they have done better? Not by much IMO. Every misstep with Chinese characteristics is being repeated just as worst in other countries with their cultural characteristics. The overall response as been not as agile (if there a response at all), despite having ample notice and more information.
The retrospect of this global health crisis is going to be interesting, China and a handful of islands managed to successful crush the curve, complacent developed countries may or may not successful spread the curve, and all the developing countries get rapid herd immunity because like the Spanish flu, they have no other choice. 1.4 billion people without herd immunity among a globalized world with immunity is going to be a conundrum though.