The context of the Tom Lehrer song is the fact that the People's Republic of China had tested a nuclear weapon in 1964. So the fact that they would be interested in a long-range rocket program — even though they were not a major global superpower at the time — was a common one. The fact that China could do all of this despite relative poverty and being in the middle of the chaos of the Cultural Revolution is part of the shock of the 1960s proliferation fears, a signal that nuclear weapons were not merely for the superpowers (see Lehrer's "Who's Next?" for more on this theme).

But to answer your specific question. I don't know the first point at which someone suggested China had the potential to be a superpower. But it is of some interest that in the interwar period, the white supremacist Lothrop Stoddard more or less made this point, in his The Rising Tide of Color (1920). Stoddard's work is seen as an incredibly important work in transforming the discourse of white supremacy from the "divide up the whites" approach of his mentor, Madison Grant (which was focused on different gradations of whiteness, and anti-semitism) to the "bicolor" approach that would become dominant in the wartime period and beyond (focused on a unified "white" versus non-white approach). Stoddard's book argues at some length that global trends were working against whiteness, and saw China in particular as a major threat. In short, he argued that the Chinese are perfectly capable of adapting to European-style models of industrialization, and once they do, they will be unstoppable. A representative quote:

At the moment, the "opening" of the Far East was hailed by white men with general approval, but of late years many white observers have regretted this forcible dragging of reluctant races into the full stream of world affairs. As an Australian writer, J. Liddell Kelly, remarks: "We have erred grievously by prematurely forcing ourselves upon Asiatic races. The instinct of the Asiatic in desiring isolation and separation from other forms of civilization was much more correct than our craze for imposing our forms of religion, morals, and industrialism upon them. It is not race-hatred, nor even race-antagonism, that is at the root of this attitude; it is an unerring intuition, which in years gone by has taught the Asiatic that his evolution in the scale of civilization could best be accomplished by his being allowed to develop on his own lines. Pernicious European compulsion has led him to abandon that attitude. Let us not be ashamed to confess that he was right and we were wrong." [...]

Certainly no one has ever denied the Chinaman's extraordinary economic efficiency. Winnowed by ages of grim elimination in a land populated to the uttermost limits of subsistence, the Chinese race is selected as no other for survival under the fiercest conditions of economic stress. At home the average Chinese lives his whole life literally within a hand's breadth of starvation. Accordingly, when removed to the easier environment of other lands, the Chinaman brings with him a working capacity which simply appalls his competitors. That urbane Celestial, Doctor Wu-Ting-Fang, well says of his own people: "Experience proves that the Chinese as all-round laborers can easily outdistance all competitors. They are industrious, intelligent, and orderly. They can work under conditions that would kill a man of less hardy race; in heat that would kill a salamander, or in cold that would please a polar bear, sustaining their energies, through long hours of unremitting toil with only a few bowls of rice." [...]

We whites will have to abandon our tacit assumption of permanent domination over Asia, while Asiatics will have to forego their dreams of migration to white lands and penetration of Africa and Latin America. Unless some such understanding is arrived at, the world will drift into a gigantic race-war - and genuine race-war means war to the knife.

I quote this at length just so one can see how much of this is mirroring the kinds of rhetoric we still see today in the fretting hands of Europeans, albeit commentators on this today usually have drained their discussions of such over and vile discussions about race (though one sometimes suspects they are lurking just below the surface). Stoddard amply quotes other commentators from the early 1900s who see things similar to him — the fear of the rise of the "Chinaman," having been disturbed from a "slumber" by foolish Europeans, is one that seems to have been fairly common among urbane commentators at the time.