With the rollout of Covid-19 vaccines, a light has appeared in the darkness. A hard winter lies ahead, but this pandemic will soon be over.

How can this be happening only 10 months after the first Covid death in the U.S., rather than the 10 years it took to develop a vaccine for measles? Nine months ago, Anthony Fauci stated unambiguously: “It will take at least a year and a half to have a vaccine we can use.” The public-health community dismissed that as a fantasy. A co-inventor of the rotavirus vaccine, Paul Offit, noted: “When Dr. Fauci said 12 to 18 months, I thought that was ridiculously optimistic.” A New York Times vaccine timeline went further, declaring: “The grim truth behind this rosy forecast is that a vaccine probably won’t arrive any time soon.”

Those naysayers have been proved wrong and it’s worth considering why. Let me invite the reader to answer a short quiz. When in the months ahead you are vaccinated, to whom should you be most thankful for making this possible?

• The initiative forwarded by the United Nations, Group of 20, World Health Organization and COVAX—an affiliate of WHO and the Coalition for Epidemic Preparedness Innovations—that called for “a ‘people’s vaccine’ available and affordable for everyone, everywhere,” in the words of U.N. Secretary-General António Guterres ?

• Foundations and donors, including the consortium led by the Gates Foundation that established the CEPI (the “alliance to finance and coordinate the development of new vaccines”) at Davos, Switzerland, in 2017?

• Leaders of federal agencies, including the directors of the Centers for Disease Control and Prevention, Food and Drug Administration, and National Institute of Allergy and Infectious Diseases, the health and human services secretary and the assistant secretary for health?

• The hundreds of medical and public health schools, their associated research labs and hospitals, and the tens of thousands of epidemiologists, virologists and other experts who have been talking endlessly about this plague?

• President Trump’s Operation Warp Speed, led by Moncef Slaoui —a controversial former head of vaccine development at the pharmaceutical company GlaxoSmithKline, which has delivered more vaccines than any other company in the world—which gave billions of taxpayer dollars to biotech and pharmaceutical companies to speed vaccine development and manufacture doses in advance in case a vaccine proved effective?

• Private, profit-seeking corporations including Pfizer, BioNTech, Moderna, AstraZeneca, Novavax and their counterparts?

Failure is an orphan; victory has a hundred fathers. In this case, success is certain to have thousands of paternity claimants. Many of those listed above will credibly claim to have contributed. But if this were a court of law allocating liability for damage done by a medicine, rather than a grateful public offering thanks, which of the actors would be held most responsible? Assuming all other claimants had done precisely what they did in this case—except for one—what is the likelihood that vaccines would be available today?

The answer is as clear as it will be uncomfortable to some readers. Had the WHO and Gates Foundation not existed, there would have been little difference in the availability of the vaccine. Had all of the departments and agencies in the U.S. government been on autopilot, this miraculous development would never have happened. This bureaucracy—including the CDC, FDA and HHS—was unable to provide a coronavirus test for several months after South Korea, Singapore and others were conducting extensive testing under their public-health responses.

Universities are rightly claiming to have built the foundations of knowledge without which other researchers couldn’t have sequenced the virus’s genome or developed mRNA delivery systems necessary to Pfizer and Moderna’s vaccines. But holding the pre-Covid base of knowledge constant, these scholarly researchers could have slept through the pandemic and it would have made little difference.

There are clearly only two primary causes behind the Covid-19 vaccine. The first was the capitalist system, which facilitated competition between private, profit-seeking biotech and pharmaceutical companies to produce a lifesaving product.

Like charities, universities, government agencies and pretty much everyone else, these organizations want to do good. But companies like Germany-based BioNTech, its Boston-based competitor Moderna, and the pharmaceutical giant Pfizer have also been racing for a pot of gold at the end of this rainbow. There would be no Covid-19 vaccine today had there been no venture capitalists prepared to invest before a product or profit was visible, no corporate leadership willing to double down with the companies’ own money in the spring to fund a crash effort to produce a vaccine by year-end, and no researchers pursuing a dream about mRNA as an unprecedented route for vaccines.

Second is Operation Warp Speed. Had Mr. Trump not created the initiative, appointed as its leader a man who knows the vaccine development world, and given him license to spend $10 billion outside normal contracting procedures, Covid-19 vaccines would still be only works in progress. Even after they were finally approved, the vaccines’ distribution could have been long delayed. Imagine a world in which Mr. Trump had not appointed as deputy head of the operation a general who knows logistics and had the authority to write contracts with FedEx and UPS to book space on their airplanes and in their network of distribution centers.

So as Americans now look forward to getting vaccinated and resuming our normal lives, we should pause to give thanks to a remarkable group of scientists and entrepreneurs whose capitalism-fed competitive drive pushed them to venture into the unknown—for fortune and fame. And to a deeply flawed, often dysfunctional disrupter in chief who in this case certainly did a good thing.

Mr. Allison, a professor of government at Harvard, is author of “Destined for War: Can America and China Escape Thucydides’s Trap?” (2017).