Accurate and efficient prediction of levitation air-gap responses is important for the dynamic assessment of electromagnetic suspension (EMS) maglev systems. However, repeated high-fidelity vehicle–guideway–electromagnetic simulations are computationally expensive, while conventional sequence models have limited ability to preserve vibration spectral characteristics. This study proposes a physics-guided Residual Discrete Cosine Transform Spectral Neural Operator (DCT-SNO) to learn the function-to-function mapping from track irregularity to time-domain air-gap response. The model employs a real-valued DCT spectral operator with learnable weights restricted to retained low-order modes, thereby embedding the low-frequency-dominant characteristic of maglev dynamics, while a residual time-domain branch captures nonlinear response features. The model is trained and evaluated using high-fidelity UM–Simulink co-simulation data covering multiple track-irregularity spectra and operating speeds of 300–500 km/h. Results show that DCT-SNO accurately reconstructs held-out air-gap responses, preserves characteristic narrowband peaks and frequency-domain energy distributions, and achieves better spectral consistency than FNO and recurrent baselines. It also reduces inference latency by approximately one order of magnitude relative to FNO, demonstrating its potential as an efficient surrogate for repeated maglev dynamic-response evaluations.