Data-driven inverse design aims to identify material structures that yield targeted effective properties, but it is often hindered by limited data availability and the high cost of experiments and simulations. This challenge is particularly pronounced when the properties of interest require expensive evaluations, such as fatigue-related metrics. In this contribution, we propose a general, data-efficient framework for inverse design of structured materials that operates effectively in the small-data regime by tightly integrating numerical simulations with probabilistic machine learning. The framework follows an iterative active-learning workflow. First, material structures are represented by suitable statistical or morphological descriptors. Second, effective properties are obtained from numerical simulations. Third, Gaussian-process surrogate models are constructed to capture structure–property linkages together with quantified uncertainty. Fourth, Bayesian optimization is employed to propose new candidate descriptors that are expected to either improve target properties or maximally reduce model uncertainty. Finally, corresponding material structures are reconstructed from the proposed descriptors. These steps are repeated until convergence criteria are met, such as a reduction in predictive uncertainty or the identification of structures with desirable performance. The proposed methodology is demonstrated using spinodoid structures as a representative application. Although spinodoids are governed by only four defining parameters, they exhibit a remarkably rich variety of morphologies. This combination of low-dimensional parametrization and high morphological diversity makes spinodoids an ideal test case for data-driven inverse design in the small-data regime. By augmenting a small initial dataset with in silico-generated spinodoid structures and their simulated effective properties, the framework progressively refines the learned structure-property relationships. This enables an efficient exploration of the accessible property spectrum and the identification of candidate structures with potentially improved mechanical performance while minimizing the number of costly evaluations.