Soft actuators using pressurized air are being widely used due to their inherent compliance, conformability and customizability. These actuators are powered and controlled by pneumatic supply systems (PSSs) consisting of components such as compressors, valves, tubing and reservoirs. Regardless of the choice of actuator, the PSS critically affects overall performance of soft robots because it governs the soft actuator pressure dynamics and thereby, the general dynamic behaviour. While selecting and controlling PSS components for meeting desired soft actuator performance, specifications such as PSS mass, volume and duration of operation must also be considered. Currently, there is no comprehensive study on PSS optimization for meeting dynamic performance and PSS specifications, due to limited understanding of soft actuator pressure dynamics, large solution space for PSSs, and variability in soft actuators. By considering critical parameters of PSS and soft actuators, we introduce and demonstrate PSS parameter optimization. We propose a normalized model for soft actuator pressure dynamics and quantify the relationship between PSS parameters, soft actuator design parameters and dynamic performance metrics of rise time, fall time and actuation frequency. Using these results, we optimally select and control PSS components to meet desired soft actuator performance for a soft exosuit, while minimizing mass of selected components. The measured pressure response with this prototype agrees well with simulations, with root mean square errors under 5.2%. This work is a step towards furthering the scope of soft robotics, as it enables PSS optimization, for meeting the desired soft actuator performance while also addressing PSS specifications.