If you have to pick a single decade, it was the 1980s.

Sorry for the text wall, but the full story is a little messier than that.

Even during the heyday of European imperialism, when its science and technology let it run roughshod over most of the world, some people saw that China was already a superpower in waiting. The UK didn't so much win its war against the Qing Empire as use its superior force projection to threaten the southern tax flow through Nanjing, bringing the Manchus to the table. Then, in the 1850s, an utterly massive flood of the Yellow River (swinging it from south to north of the Shandong Peninsula) and the Taipings following close behind completely wrecked the state. Cixi's resistance to Li Hongzhang & co's proposals for industrial reform didn't help, and soon you had everyone but the Americans cutting up the country into spheres of influence and everyone including the Americans angling for trade privileges, mining rights, railroad contracts, &c. The Chinese were blessed that their overthrow of the Manchus (which entailed even greater weakness as it kicked off four decades of civil wars) was timed just before Europe's self-immolation in the 1910s. (In the fullness of time, the failure to fully colonize China is going to turn out to have been perhaps the single biggest consequence of WWI, so that's a good second-best answer to your question.)

The Chinese themselves would say it was the 1940s

because Sun Yat-sen started the rebirth of China but Mao was the one who had to win all those civil wars and fight off the imperialists to finish it. Really, the warlord era and WWII and the Civil War and Mao's early policy failures all crushed the country, with Mao's wounds being almost entirely self-inflicted. At the same time, he reunited almost all of the country (the PRC and ROC both consider Taiwan just a wayward province), was strong enough to end foreign invasions (despite MacArthur's best attempts to make it happen), rebuilt the railroads and tamed the rivers (finally!), and got Nixon to sign off on recognizing the PRC as the actual Chinese government at the UN. It's just that everyone underneath him was equally secure in their poverty.

Deng Xiaoping

is the one who changed that. He and his supporters had been jailed during the Cultural Revolution, and at Mao's death there was a real struggle over where the country would go through the late '70s. If it had ground on the way it had been, it would've gone the way of the Soviet Union and today would be a gigantic form of what you see in North Korea. If control had been wrested by truly liberal reformers, it would have shunted into a market economy too quickly, been prey to its own elites and foreign capital, and today it would be an even more monstrous kleptocracy than Russia is. After he won the power struggle, what Deng & his guys did instead was reform slowly and watchfully from the ground up beginning with pilot projects; they brought in foreign capital but demanded it partner with and train domestic businesses; they focused step by step on moving up the technology ladder so Chinese manufacturing didn't remain in low-margin textiles and toys; they kept wages low but slowly kept improving quality of life in the form of better hospitals, schools, etc.

(In China, you don't talk about 1989 but that was important for the country's trajectory, too: the students were never the threat. Li Peng & co. sent the army in only after the kids'd started teaming up with the workers unhappy that market reforms cost them their jobs at the state companies or forced them to work harder or retrain. There was no way―given China's last two centuries―the government was ever going to let itself collapse, leaving China in another civil war or weak in the face of hostile foreigners. And the other side never wanted to be a second US: the workers at least were in the streets for a return to Maoist orthodoxy. So... terrible tragedy but another thing that kept China from collapsing like Russia or imploding like North Korea.)

Now, because Deng's reforms were slow and careful and because it took time to move up that development chain, the GDP numbers will tell you that China took off in the 1990s and 2000s. China still can't make its own world-class jet engines, Russia is able to make a great profit on forcing them to buy entire fighters just to be able to remove and refit the engines, and the US still outspends them both on defense by an order of magnitude. Trump mostly won his trade war, the coronavirus outbreak has hurt the country's numbers, and the screwups in Hong Kong have delayed the great national priority―a peaceful reintegration of Taiwan Island―by decades. China's got an aircraft carrier and some international contracts denominated in RMB but doesn't have anything like the US's force projection capability or alliances. It's not a full superpower yet.

But the fact of the matter is that China has been one of the world's superpowers from nearly the dawn of civilization. Modernity curb stomped it, but it's the size of Europe on its own, has the population of Africa on its own, and has a culture that prizes education and values group success. It was always going to find its own level, given peace, security, and some ability to profit from its own work. What you see right now is the result of the programmes laid out in the '80s.

[Addendum: The idea that WTO membership was responsible is essentially the idea that China required the US's help to improve itself. On the one hand, that's nonsense and the improvements would've come on in any case. On the other, US and WTO membership definitely sped things up by decades and helped improve Chinese living standards much faster... The thing is, though, that the whole deal that the US thought it was getting was that increasing trade would necessarily involve a more US-like China that would eventually ease state controls and one party rule and ideally provoke a Soviet-style collapse. That unquestionably hasn't happened, and the reason is because of the slow and careful management Deng & his successors took to the whole operation. So, again, the '80s.]