We have compelling evidence for stellar-mass black holes (BHs) of ~5-80 M_sun that form through the death of massive stars. We also have compelling evidence for so-called supermassive BHs (10^5-10^10 M_sun) that are predominantly found in the centers of galaxies. We have very good reason to believe there must be BHs with masses in the gap between these ranges: the first ~10^9 M_sun BHs are observed only hundreds of millions of years after the Big Bang, and all theoretically viable paths to making supermassive BHs require a stage of "intermediate" mass. However, no BHs have yet been reliably detected in the 100-10}^5 M_sun mass range. Uncovering these intermediate-mass BHs of 10^3-10^5 M_sun is within reach in the coming decade. In this white paper we highlight the crucial role that 30-m class telescopes will play in dynamically detecting intermediate-mass black holes, should they exist.