<p>Ecosystems with higher prey diversity often exhibit greater resilience to environmental disturbances. Unlike previous studies, the originality of our work lies in the simultaneous incorporation of both gestation and maturation delays within the predator-prey system. This study examines a two-prey predator model incorporating a Holling Type-II functional response with three distinct delays, representing the maturation periods of each prey species and the gestation period of the predator. Our findings highlight the intricate interplay between maturation and gestation delays in regulating population oscillations and predator efficiency. We establish conditions for the stability of feasible equilibrium points and reveal the influence of delays on predator-prey interactions. In addition, statistical methods are developed for parameter estimation and prediction of capture probabilities between the two prey species. To illustrate the practical applicability of the theoretical results, we present numerical simulations, demonstrating the effectiveness of the model in capturing the dynamics of such ecological systems. </p>