In this work, we systematically investigate the impact of ambient noise intensity on the rate modifications of ground-state chemical reactions in an optical cavity under vibrational strong-coupling conditions. To achieve this, we utilize a numerically exact open quantum system approach-the hierarchical equations of motion in twin space, combined with a flexible tree tensor network state solver. Our findings reveal a stochastic resonance phenomenon in cavity-modified chemical reactivities: an optimal reaction rate enhancement occurs at an intermediate noise level. In other words, this enhancement diminishes if ambient noise, sensed by the cavity-molecule system through cavity leakage, is either too weak or excessively strong. In the collective coupling regime, when the cavity is weakly damped, rate enhancement strengthens as more molecules couple to the cavity. In contrast, under strong cavity damping, reaction rates decline as the number of molecules grows.