China did it to themselves in the first place. They silenced the early warnings about the epidemic, and did not acknowledge anything until it was already too late in Wuhan. It could have ended right there had they been more serious to begin with.
Weeks after the total shutdown in Wuhan, the President of the United States went on TV to say that it was little more than a flu. Same with the leaders in Europe. I'd say they absolutely dropped the ball.
As far as I can tell, the only way to contain this would've been if every county on the planet had cut off travellers from China in January and tracked down and quarantined those already in the country - something China actively campaigned against with the support of the WHO. All of the countries that have contained this relied on that combined with contact tracing and testing once one became available, even China itself. Just testing and tracing alone hasn't worked anywhere. So it's less "wasted all the time China gave us" and more "trusted what China was saying, not what they were doing".
Except the country that handled it best (South Korea) didn't ban travel from China and the president even publicly declared it won't ban travel from China saying things like "If Korea bans China then other countries may ban Korea" despite mass protests.
South Korea hasn't contained the virus yet. They've done a good job at squashing the big cluster in Daegu, partly due to luck (the index patient didn't meet the criteria for testing but got tested anyway), and their numbers look promising. However, Italy's numbers looked good right up until they didn't. The fear is that there are a bunch of other clusters spread throughout the country that are slowly bubbling away, too many to apply contact tracing to, and it looks like there's evidence that is becoming the case: https://www.npr.org/sections/goatsandsoda/2020/03/10/8128651...
There's a huge difference between looking good with small numbers because you haven't done testing like in much of Europe or NA vs looking good because you've blanketed the country in tests and are seeing recoveries outstrip infections.
Italy also wasn't testing. Their signal was hospitals overflowing with dying patients. So it's unlikely that SK is missing significant numbers of cases. If they were their hospitals would be overflowing.
This dress rehearsal hasn’t gone well.