The large cutout structure is a key component in the bottom skin of an airplane wing, and is susceptible to developing fatigue cracks under service loads. Early fatigue crack detection is crucial to ensure structural safety and reduce maintenance costs. Nonlinear Lamb wave techniques show significant potential in microcrack monitoring. However, nonlinear components are often relatively weak. In addition, a large cutout structure introduces complex boundary conditions for Lamb wave propagation, making nonlinear Lamb wave monitoring more challenging. This article proposes an integrated data processing method, combining phase inversion with continuous wavelet transform (CWT) to enhance crack detection in complex structures, with phase-velocity desynchronization adopted to suppress the material nonlinearity. Experiments on a large cutout aluminum alloy plate with thickness variations were conducted to validate the proposed method, and the results demonstrated its effectiveness in detecting fatigue cracks. Furthermore, this study found that nonlinear components are more effective than linear components in monitoring closed cracks.