MOTIVATION: Intratumor heterogeneity arises from ongoing somatic evolution and complicates cancer diagnosis, prognosis, and treatment. Reconstructing evolutionary dynamics typically requires spatiotemporal samples, which are often unavailable in clinical settings. Computational approaches that can infer tumor evolutionary history from single-timepoint bulk sequencing data remain limited. RESULTS: We present estimating evolutionary events through single-timepoint sequencing (TEATIME), a novel computational framework that models tumors as mixtures of two competing cell populations: an ancestral clone with baseline fitness and a derived subclone with elevated fitness. Using cross-sectional bulk sequencing data, TEATIME estimates mutation rates, timing of subclone emergence, relative fitness, and number of generations of growth. To quantify intratumor fitness asymmetries, we introduce a novel metric-fitness diversity-which captures the imbalance between competing cell populations and serves as a measure of functional intratumor heterogeneity. Applying TEATIME to 33 tumor types from The Cancer Genome Atlas, we revealed divergent as well as convergent evolutionary patterns. Notably, we found that immune-hot microenvironments constraint subclonal expansion and limit fitness diversity. Moreover, we detected temporal dependencies in mutation acquisition, where early driver mutations in ancestral clones epistatically shape the fitness landscape, predisposing specific subclones to selective advantages. These findings underscore the importance of intratumor competition and tumor-microenvironment interactions in shaping evolutionary trajectories, driving intratumor heterogeneity. Lastly, we demonstrate that TEATIME-derived evolutionary parameters and fitness diversity offer novel prognostic insights across multiple cancer types. AVAILABILITY AND IMPLEMENTATION: R implementation of TEATIME is available on GitHub (https://github.com/liliulab/TEATIME) and Zenodo (https://zenodo.org/records/17422174).