A dozen of America’s top scientists and a collection of billionaires and industry titans say they have the answer to the coronavirus pandemic, and they found a backdoor to deliver their plan to the White House.

The eclectic group is led by a 33-year-old physician-turned-venture capitalist, Tom Cahill, who lives far from the public eye in a one-bedroom rental near Boston’s Fenway Park. He owns just one suit, but he has enough lofty connections to influence government decisions in the war against Covid-19.

These...