Background: We assessed the prognostic value of the pan-immune–inflammation value (PIV), systemic immune–inflammation index (SII), lung immune prognostic index (LIPI), and c-reactive protein–albumin–lymphocyte (CALLY) index in advanced non-small cell lung cancer (NSCLC) treated with first-line immune checkpoint inhibitor (ICI)-based therapy. Methods: This multicenter retrospective study included 161 patients who received ICI monotherapy, chemoimmunotherapy, or dual ICI therapy. The objective response rate (ORR), clinical benefit rate (CBR), progression-free survival (PFS), and overall survival (OS) were analyzed using Kaplan–Meier and Cox regression models. Results: A high CALLY index was associated with a significantly higher CBR (82.1% vs. 59.5%; p = 0.015), longer PFS (14.95 vs. 7.13 months; p = 0.002), and longer OS (25.79 vs. 13.24 months; p = 0.003). In the multivariable analyses, a high CALLY index remained independently associated with improved PFS (HR = 0.52, p = 0.006) and OS (HR = 0.53, p = 0.010), whereas a high SII was independently associated with poorer PFS (HR = 1.74, p = 0.021) and OS (HR = 1.90, p = 0.009). PIV and LIPI were not independently associated with survival outcomes. Conclusions: SII and the CALLY index emerged as independent prognostic biomarkers in advanced NSCLC receiving first-line immunotherapy-based treatment. The CALLY index showed the strongest and most consistent association with clinical benefit, PFS, and OS.