The dynamic interactions between an evolving malignancy and the adaptive immune system generate diverse evolutionary trajectories that ultimately result in tumor clearance or immune escape. Here, we create a simple mathematical model coupling T-cell recognition with an evolving cancer population that may randomly produce evasive subclones, imparting transient protection against the effector T cells. T-cell turnover declines and evasion rates together explained differences in early incidence data across almost all cancer types. Fitting the model to TRACERx evolutionary data argued in favor of substantial and sustained immune pressure exerted upon a developing tumor, suggesting that clinically observed incidence is a small proportion of all cancer initiation events. This dynamical model promises to increase our quantitative understanding of many immune escape contexts, including cancer progression and intracellular pathogenic infections.Significance:The early cancer–immune interaction sculpts intratumor heterogeneity through the selection of immune-evasive clones. This study provides a mathematical framework for investigating the coevolution between an immune-evasive cancer population and the adaptive immune system.