We propose a modified population-based susceptible-exposed-infectious-recovered (SEIR) compartmental model for a retrospective study of the COVID-19 transmission dynamics in India during the first wave. We extend the conventional SEIR methodology to account for the complexities of COVID-19 infection, its multiple symptoms, and transmission pathways. In particular, we consider a time-dependent transmission rate to account for governmental controls (e.g., national lockdown) and individual behavioral factors (e.g., social distancing, mask-wearing, personal hygiene, and self-quarantine). An essential feature of COVID-19 that is different from other infections is the significant contribution of asymptomatic and pre-symptomatic cases to the transmission cycle. A Bayesian method is used to calibrate the proposed SEIR model using publicly available data (daily new tested positive, death, and recovery cases) from several Indian states. The uncertainty of the parameters is naturally expressed as the posterior probability distribution. The calibrated model is used to estimate undetected cases and study different initial intervention policies, screening rates, and public behavior factors, that can potentially strike a balance between disease control and the humanitarian crisis caused by a sudden strict lockdown.