He grew up in Potomac, Maryland. He graduated from Stanford University in 2005 with a bachelor's degree in physics and a doctorate in physics from MIT in 2012, where his research was in astrophysics. Williams is a board-certified medical physicist, completing his residency training at Harvard Medical School before joining the faculty as a clinical physicist and researcher. He most recently worked as a medical physicist in the Radiation Oncology Department at the Brigham and Women's Hospital and Dana-Farber Cancer Institute in Boston. He was the lead physicist for the Institute's MRI-guided adaptive radiation therapy program. His research focused on developing image guidance techniques for cancer treatments.