In the US, New York had also to respond hard to the first wave.
Italy and US compared in deaths per million due to Covid-19:
https://ourworldindata.org/coronavirus-data-explorer?zoomToS...
China, having the hardest and the most restrictive lockdowns, managed something even better than both: binging the numbers to effectively zero, very early. They also managed to maintain the minimum of new cases by mass testing actions when there was a suspicion of the outbreak:
https://www.bbc.com/news/world-asia-54504785
"Covid-19: China's Qingdao to test nine million in five days"
And they have still kept wearing the masks this year, whenever they aren't alone, if I understand it correctly.
We also know that such kind of mass testing can be done in Europe too, if mandated, as in Slovakia:
https://www.thetimes.co.uk/article/slovakia-offers-proof-tha...
So, no, it wasn't about the vaccines up to now. The measures simply work, proved in Europe, and even in the US, when they are consistently introduced. As simple as that.
Though given how hush hush China is about everything, it's also possible they've had a vaccine they've been using on their population for a while and just deigned not to tell or share.