Estimating an epidemic's trajectory is crucial for developing public health responses to infectious diseases, but case data used for such estimation are confounded by variable testing practices. We show that the population distribution of viral loads observed under random or symptom-based surveillance, in the form of cycle threshold (Ct) values obtained from reverse-transcription quantitative polymerase chain reaction testing, changes during an epidemic. Thus, Ct values from even limited numbers of random samples can provide improved estimates of an epidemic's trajectory. Combining data from multiple such samples 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 offer alternative approaches for real-time estimates of epidemic trajectories for outbreak management and response.