Early detection of infectious diseases such as Covid-19 can limit transmission and curb pandemics. This study proposes EarlyDetect, an end-to-end framework for early Covid-19 detection using heart rate and step data collected passively from consumer-grade health trackers. A key challenge in early Covid-19 detection is determining the optimal amount of historical data (e.g., past days) a machine learning model should analyze to achieve the earliest possible, yet accurate, infection detection. Leveraging Reinforcement Learning-based Early Time Series Classification, EarlyDetect extracts 45 digital biomarkers (daily steps, daytime/nighttime HR, mesor, sedentary time), and feeds them into a deep Multi-layer Perceptron neural network model trained using Double Deep Q-Network. At each iteration, EarlyDetect dynamically decides whether to wait for more data or proceed with classifying the window of data observed so far. A novel reward function ensures early yet accurate classification in imbalanced class distributions. Using heart rate and steps values over 72 hours lookback window, EarlyDetect achieves an accuracy of 0.8 (95% CI 0.71-0.89), AUC-ROC of 0.73 (95% CI: 0.6-0.86), an earliness of 0.07 (95% CI: 0.05-0.09), thus requiring up to 86% less data than existing methods while predicting Covid-19 status 50% earlier (smaller detection window). Performance on two Covid-19 datasets was encouraging, identifying 61% and 46% of Covid+ cases before the coronavirus reached peak transmissibility. EarlyDetect is a significant advancement in early infectious disease screening, and is the first method to dynamically determine an optimal lookback window size for Covid-19 detection from physiological signs on imbalanced datasets using Reinforcement Learning-based Early Time Series Classification.