It was early October 2019 and Uğur Şahin was standing in a Kansas City, Mo., parking lot, sweating under the blazing midafternoon sun. He and a few colleagues had spent weeks crisscrossing the U.S. and visiting different cities in Europe. They were trying to drum up investor interest in the initial public offering of BioNTech SE, the German biotechnology company Dr. Şahin had started. The trip wasn’t going well.

The investors liked Dr. Şahin but had misgivings about his company, which was developing vaccines and treatments to combat various cancers and infectious diseases. One of its approaches was to use a molecule called messenger RNA to carry instructions into the body, enabling it to ward off illness. Dr. Şahin had spent more than two decades researching how to teach the immune system to fight disease. He needed an IPO to help make it happen, but investors were balking—including the Kansas City mutual-fund manager he had just met.