Operator learning approaches, exemplified by the Fourier Neural Operator (FNO), provide fast approximations of PDE solution operators and are attractive surrogates for accelerating computer-aided engineering workflows. In topology optimization, applying such surrogates to iterative loops raises a robustness issue: the distribution of designs encountered during optimization can drift away from the training distribution. This out-of-distribution (OOD) shift may increase objective-value errors and corrupt the relative ordering of candidate designs, i.e., the ranking that guides step acceptance and design updates. As a consequence, optimization may become unstable or converge to a poor local minimum. We address this challenge by proposing a training data generation strategy based on random density fields synthesized in the spectral domain. By controlling spatial frequency content and correlation length, the generator produces diverse density patterns that better cover intermediate and near-binary configurations encountered in topology optimization. The FNO is trained to map density fields to stress and strain fields. The strain energy is computed as a surrogate objective via domain integration, and design sensitivities are obtained through automatic differentiation, enabling end-to-end gradient-based topology optimization without repeated FEM solves. Training data are generated from the proposed random density-field generator. For OOD evaluation, we use binary (0–1) structures produced by the generative model Optimize Any Shape (Nobari et al.), which differs from the training distribution. Generalization is quantified by (i) the error of representative objective values (e.g., strain energy) with respect to FEM reference solutions and (ii) Spearman’s rank correlation coefficient to assess ranking consistency. We benchmark FNO against a ResNet-based surrogate. Preliminary results show that the proposed data generation improves both objective accuracy and ranking preservation under OOD conditions, indicating that data design is a key lever for reliable surrogate-assisted topology optimization. The approach can reduce expensive FEM calls while maintaining optimization stability and decision quality.