Estimating an epidemic's trajectory is crucial for developing public health responses to infectious diseases, but incidence data used for such estimation are confounded by variable testing practices. We show instead that the population distribution of viral loads observed under random or symptom-based surveillance, in the form of cycle threshold (Ct) values, changes during an epidemic and that Ct values from even limited numbers of random samples can provide improved estimates of an epidemic's trajectory. Combining multiple such samples and the fraction positive improves the precision and robustness of such estimation. We apply our methods to Ct values from surveillance conducted during the SARS-CoV-2 pandemic in a variety of settings and demonstrate new approaches for real-time estimates of epidemic trajectories for outbreak management and response.