Fused Deposition Modeling (FDM) is a type of additive manufacturing (AM) that has received significant interest from researchers and industries due to its flexibility in design, efficient use of materials, and affordable costs. In this paper, the main objective is to investigate the influences of FDM process parameters on the flexural properties as well as the accuracy of the final part made from polyethylene terephthalate glycol (PETG) material, which is widely used for 3D printing due to its strength and ease of use. A response surface methodology (RSM) approach based on a Box–Behnken design was employed, with three key process parameters: infill line distance, wall line count, and build plate temperature. The analysis of the data indicated that all three parameters affected the inherent characteristics of the printed parts, including mechanical and dimensional characteristics of the printed parts. The build plate temperature was identified as the most significant parameter, contributing 53% of the variability in the flexural strength of the printed specimens and 39.7% to deviation in the dimensional accuracy of the specimens, as indicated by the analysis of variance (ANOVA). A comparison between the predicted values of the model and the corresponding experimental results showed the suitability of the developed model with high accuracy. The maximum percentage errors observed in this study were 3.4% for the flexural strength and 7.5% for the dimension accuracy, establishing the efficacy of the optimization technique. These outcomes are meaningful to understand the influences of the process parameters on material response and offer a systematic approach to develop structurally enhanced PETG parts with improved mechanical characteristics and geometric dimensions.