SARS-CoV-2 variants have demonstrated distinct epidemiological patterns and clinical presentations throughout the COVID-19 pandemic. Understanding variant-specific differences at the respiratory epithelium is crucial for understanding their pathogenesis. Here, we utilized human nasal organoid air–liquid interface (HNO-ALI) cell cultures to compare the viral replication kinetics, innate immune response, and epithelial damage of six different strains of SARS-CoV-2 (B.1.2, WA, Alpha, Beta, Delta, and Omicron). All variants replicated efficiently in HNO-ALIs, but with distinct replication kinetic patterns. The Delta variant exhibited delayed replication kinetics, achieving a steady state at 6 days post-infection compared to 3 days for other variants. Cytokine analysis revealed robust pro-inflammatory and chemoattractant responses (IL-6, IL-8, IP-10, CXCL9, and CXCL11) in WA1, Alpha, Beta, and Omicron infections, while Delta significantly dampened the innate immune response, with no significant induction of IL-6, IP-10, CXCL9, or CXCL11. Immunofluorescence and H&E analysis showed that all variants caused significant ciliary damage, though WA1 and Delta demonstrated less destruction at early time points (3 days post-infection). Together, these data show that, in our HNO-ALI model, the Delta variant employs a distinct “stealth” strategy characterized by delayed replication kinetics and epithelial cell innate immune evasion when compared to other variants of SARS-CoV-2, potentially explaining a mechanism that the Delta variant can use for its enhanced transmissibility and virulence observed clinically. Our findings demonstrate that variant-specific differences at the respiratory epithelium could explain some of the distinct clinical presentations and highlight the utility of the HNO-ALI system for the rapid assessment of emerging variants.