Early time classification algorithms aim to label a stream of features without processing the full input stream, while maintaining accuracy comparable to that achieved by applying the classifier to the entire input.In this paper, we introduce a statistical framework that can be applied to any sequential classifier, formulating a calibrated stopping rule. This data-driven rule attains finite-sample, distribution-free control of the accuracy gap between full and early-time classification. We start by presenting a novel method that builds on the Learn-then-Test calibration framework to control this gap marginally, on average over i.i.d. instances.As this algorithm tends to yield an excessively high accuracy gap for early halt times, our main contribution is the proposal of a framework that controls a stronger notion of error, where the accuracy gap is controlled conditionally on the accumulated halt times.Numerical experiments demonstrate the effectiveness, applicability, and usefulness of our method. We show that our proposed early stopping mechanism reduces up to 94\% of timesteps used for classification while achieving rigorous accuracy gap control.