Virtually any country that achieves political stability and effective institutions experiences rapid development in the modern world with open knowledge and trade networks.
There is nothing special about central planning in that manner that a laissez-faire economy would also achieve at that low development.
That's quite a misattribution of success. The Russian empire was politically stable throughout the industrial revolution era, and yet lagged behind other great powers substantially. The Soviet revolution, of course, ushered in a famously politically unstable era with regular, massive purges. Meanwhile, there are many relatively politically stable countries that never managed to become especially industrialised over a period of many decades even up to the modern day, for example Mexico.
There's also a difference between "any country can rapidly develop", and what the USSR did, reaching a superpower status only two countries in the world achieved. For example, the USSR produced 80,000 T-34 medium tanks to the US's 50,000 Sherman tanks and Germany's 8500 PzIV tanks, and it was superior to both. That is a ridiculous feat, and it happened in the middle of a massive invasion that forced the relocation of huge swathes of industry to boot. The USSR was also the first to most space achievements, and it was second to develop nuclear weapons. The USSR did not just catch up to "any industrialised nation", it surpassed them all completely other than the US.