This paper aimed to evaluate the effects of different preparation parameters, including agitation speed, agitation time, and chilling temperature, on the structural and mechanical properties of a novel gelatin/elastin/sodium hyaluronate tissue engineering scaffold, recently developed by our research group. Fabricated using a combination of foaming and freeze-drying techniques, the scaffolds were assessed to understand how these parameters influence their morphology, internal microstructure, porosity, mechanical properties, and degradation behavior. The fabrication process used in this study involved preparing a homogeneous aqueous solution containing 8% gelatin, 2% elastin, and 0.5% sodium hyaluronate (w/v), which was then subjected to mechanical agitation at speeds of 500, 1000, and 1500 rpm for durations of 5, 15, and 25 min. This mixture was subsequently frozen at −20 °C and −80 °C, followed by freeze-drying and cross-linking. Morphological analyses using laser microscopy and scanning electron microscopy (SEM) demonstrated that the scaffolds had pore sizes ranging from 100 to 300 µm, which are conducive to effective cell interaction and tissue regeneration. This confirmed the efficacy of the combined foaming and freeze-drying method in creating highly interconnected porous structures. Our findings indicated that chilling temperature slightly influenced pore size. In contrast, higher agitation speeds and longer duration times led to increased porosity and degradation rate but decreased modulus. Mathematical estimators were developed for the porosity and compressive modulus of the scaffolds by statistical analysis of the preparation parameters. The estimators were validated experimentally, with the error between estimated and experimental values being less than 6% for porosity and less than 21% for compressive modulus.