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Abstract We present 307 type Ia supernova (SN) light curves from the first 4 yr of the Transiting Exoplanet Survey Satellite mission. We use this sample to characterize the shapes of the early-time light curves, measure the rise times from first light to peak, and search for companion star interactions. Using simulations, we show that light curves must have noise <10% of the peak flux to avoid biases in the early-time light-curve shape, restricting our quantitative analysis to 74 light curves. We find that the mean power-law index $t^{{\beta }_1}$of the early-time light curves isβ₁= 1.93 ± 0.57, and the mean rise time to peak is 15.7 ± 3.5 days. The underlying population distribution forβ₁may instead consist of a Gaussian component with mean 2.29, width 0.34, and a long tail extending to values less than 1.0. We find that the data can rarely distinguish between models with and without companion interaction models. Nevertheless, we find three high-quality light curves that tentatively prefer the addition of a companion interaction model, but the statistical evidence for the companion interactions is not robust. We also find two SNe that disfavor the addition of a companion interaction model to a curved power-law model. Taking the 74 SNe together, we calculate 3σupper limits on the presence of companion signatures to control for orientation effects that can hide companions in individual light curves. Our results rule out common progenitor systems with companions having Roche lobe radii >31R_⊙(separations >5.7 × 10¹²cm, 99.9% confidence level) and disfavor companions having Roche lobe radii >10R_⊙(separations >1.9 × 10¹²cm, 95% confidence level). Lastly, we discuss the implications of our results for the intrinsic fraction of single degenerate progenitor systems.