We present the first detailed study of optical absorption coefficients (OACs) in a GaAs quantum dot confined with a Woods–Saxon potential containing a hydrogenic impurity at its center. We use a finite difference method to solve the Schrödinger equation within the framework of the effective mass approximation. First, we compute energy levels and probability densities for different parameters governing the confining potential. We then calculate dipole matrix elements and energy differences, $E_{1p}-E_{1s}$, and discuss their role with respect to the OACs. Our findings demonstrate the important role of these parameters in tuning the OAC to enable blue or red shifts and alter its amplitude. Our simulations provide a guided path to fabricating new optoelectronic devices by adjusting the confining potential shape.