Japan's industrial base was built before the 40s, with an extensive domestic supply of machine tools and industrial equipment, rail infrastructure, and finished manufactured goods. Or else who do you think was building the planes, ships, and submarines that the allies were fighting on the Pacific front? Their industries were temporarily damaged by the war but it's no surprise that they'd be back to building cars within a couple decades.
They, rather than the US, were the ones who built up much of the initial industrial base of Taiwan and Korea, as part of their own colonization efforts. Not out of so much benevolence, of course.
Their skill base was intact but their industry was razed by WW2.
Either way they needed raw materials and markets to develop their industrial base and that required favorable American trade policy, $$$ and military support.
The reason these countries were allowed to do it where others are not was because the US wanted strategically placed powerful allies in the region.
There probably wouldn't be a Japanese electronics/car industry, for instance, if the Soviets hadn't spooked the the US in the 40s.