This research presents an approach to procedural circuit sizing of an operational amplifier for applications in low-frequency biomedical systems using the new powerful Improved Golden Jackal Algorithm. Traditional rule-based manual circuit sizing often falls short in efficiency due to its longer computational cost. To address this, an objective function comprising various circuit configurations and their corresponding performance metrics has been formulated and solved considering area minimization as the major goal. This is because more area directly translates to more cost. Additionally, biomedical systems are typically described by their compact size and implantable features. In order to minimize the area while maintaining a balance between the two main design parameters: noise and power, a specific approach is used as a design constraint. Simulation results and comparative study disclose the supremacy of this proposed approach when compared to state-of-the-art approaches, yielding marked enhancements in power and noise, while maintaining the trade-off and overall area. Notably, the Improved Golden Jackal Algorithm excels, achieving a remarkable circuit area of 492 µm2 while maintaining an optimal balance between noise of 136 nV and power value 6.11 µW for the desired specifications. Furthermore, validation in Cadence Virtuoso using GPDK 90 nm demonstrates the efficiency of the proposed method in real scenario with technology-bound constraints.