Systemic Inflammatory Response Syndrome (SIRS) is associated with significant morbidity and mortality in full-term newborns. This study aimed to evaluate the predictive value of the Neutrophil-to-Lymphocyte Ratio (NLR), Derived Neutrophil-to-Lymphocyte Ratio (dNLR), Platelet-to-Lymphocyte Ratio (PLR), Neutrophil, Lymphocyte, and Platelet Ratio (NLPR), AST-to-Platelet Ratio Index (APRI), and Systemic Immune–Inflammation Index (SII) in identifying the risk for SIRS development in full-term newborns. Conducted between January 2023 and January 2024, this observational cohort study compared full-term newborns diagnosed with SIRS with newborns without SIRS, measuring the inflammatory markers within the first day of life and three days post-birth. The study included 229 newborns, 81 with SIRS and 148 controls without SIRS. Statistically significant differences were observed in NLR (3.81 vs. 2.20, p < 0.0001), PLR (68.12 vs. 52.30, p < 0.0001), and liver enzymes (AST 40.96 U/L vs. 31.58 U/L, ALT 34.66 U/L vs. 22.46 U/L, both p < 0.0001) between the groups. The NLPR demonstrated substantial diagnostic value, with a sensitivity of 78.36% and specificity of 83.52% at 72 h (p < 0.0001). Regression analysis highlighted that the NLPR and SII were strongly predictive of SIRS, with the NLPR showing over three-times higher SIRS risk (HR 3.29, p < 0.0001) and SII indicating nearly 3.5 times the risk (HR 3.47, p < 0.0001). The NLPR, APRI, and SII showed similar prediction values to CRP levels measured on the first and third days of life (HR 3.16). Inflammatory markers like NLR, PLR, and systemic indices such as NLPR and SII, alongside liver function tests, are significant predictors of SIRS in full-term newborns. These findings support the integration of these markers into routine neonatal care, allowing for early identification and potentially improved management of newborns at risk for SIRS, thereby enhancing clinical outcomes.