The current study details the creation of synthetic hydroxyapatite (HAp) using a combination of catfish and bovine bones (C&B). This is done to design the optimum processing parameters and consolidate instructional strategies to develop HAp scaffolds for biomedical engineering. The HAp produced from the novel mix of the biogenic materials (C&B) was through calcination and supported with the sol-gel technique, sintering, and low-cold compaction pressure. The ideal preparation conditions were identified with the aid of the Box-Behnken statistical design in response surface methodology. To understand the physicochemical and mechanical properties of the formulation, analytical studies on the synthesized HAp were carried out. To establish a substantial relation between the physicomechanical properties of the produced HAp scaffolds, three parameters— sintering temperature, compaction loads, and holding times were used. In the evaluation, the sintering temperature was found to have the greatest impact on the material's physicomechanical properties, with compressive strength (13 MPa), porosity (49.45 %), and elastic modulus (2.216 GPa) being the most enhanced properties in that order. The physicomechanical characteristics of the HAp scaffolds were at their optimal at 900 °C, 1 h 18 min of holding time, and 311.73 Pa of compaction pressure. X-ray diffraction (XRD) and Fourier transform infrared (FTIR) results showed that powders with a dominant HAp phase were produced at all runs, including the optimum run. Therefore, using a computationally effective methodology that is helpful for novelties in biomedical engineering education, this study demonstrates the optimal process for the synthesis of a novel matrix bone-derived HAp, showing the most significant relations liable for manufacturing medically suitable HAp scaffolds from the mixture of bovine and catfish bones.