Before NASA selection, Williams moved into medical physics and radiation oncology. He completed medical physics residency training through Harvard Medical School and worked as a clinical physicist and researcher at Brigham and Women's Hospital and Dana-Farber Cancer Institute, where he contributed to MRI-guided adaptive radiation therapy. That background gave him an unusual astronaut profile: a scientist whose technical work was directly tied to both space science and advanced medical treatment.

NASA selected Williams as an astronaut candidate in 2021, and he graduated with NASA's 23rd astronaut class in 2024. NASA assigned him to Soyuz MS-28 in April 2025 for his first spaceflight, launching with Roscosmos cosmonauts Sergey Kud-Sverchkov and Sergey Mikayev to the International Space Station. The mission placed him aboard Expedition — open definition 73 and Expedition 74 as a flight engineer, where his work includes station operations, science investigations, and technology demonstrations.

Williams's active mission should be read as an in-progress spaceflight record. His total time in space is still accumulating, but his career already matters because he represents the newer generation of NASA astronauts moving from candidate training into long-duration station operations and because his path brings medical physics and astrophysics into the astronaut corps in a visible way.