The wide examination of FDM as an industrial additive manufacturing technique appears because it provides design freedom alongside improved material efficiency and reasonable cost. This study's main objective is to investigate the relationship of Fused Deposition Modeling (FDM) process parameters with the tensile properties and surface roughness of Polyethylene terephthalate glycol (PETG) parts. A response surface methodology (RSM) utilizing Box–Behnken design methodology studied three essential parameters consisting of infill density and layer height, together with plate temperature. The analysis demonstrated that layer height proved to be the main element affecting tensile strength because it contributed 80.9% of the experimental variations, while infill density stood out as the leading determinant of surface roughness, which was responsible for 78% of the contribution. Experimental testing proved that the predictive model showed accurate results when validated through measurements of tensile strength, which produced maximum errors of 1.28%, and surface roughness, which yielded maximum errors of 6.54%. A desirability analysis indicated that the ideal parameters of the roughness and tensile strength of the printed parts included an infill density of 64.24% combined with a layer height of 0.1813 mm and plate temperature of 51.46°C. These outcomes provide a comprehensive understanding of process parameter effects that result in quality PETG parts with mechanical performance. The two-axis optimization methodology for PETG also enhances its use in functional engineering systems that require simultaneous mechanical durability and manufacturing accuracy.