In this paper, an end-to-end Moon mission was simulated, encompassing both the transfer and landing phases. The emphasis was placed on utilizing techniques that are resilient to variations in boundary conditions, capable of delivering results within relatively short simulation times, yet still sufficiently accurate to support system design in the early stages of a project. For the transfer trajectory optimization, direct single shooting methods based on the Sequential Quadratic Programming (SQP) technique were employed to identify the best bi-weekly, 3-day-long launch windows throughout 2031. Subsequently, for the descent trajectory optimization, direct collocation methods based again on the SQP technique were utilized to address the impact of some critical design parameters for a lander. The key design elements that were considered are the thrust-to-mass ratio, the engine capability to change the thrust module and direction at different rates, and the propellant consumption required to execute divert maneuvers.