Reconstructing the structural geology and mineral composition of the first few kilometers of the Earth's subsurface from sparse or indirect surface observations remains a long-standing challenge with critical applications in mineral exploration, geohazard assessment, and geotechnical engineering. This inherently ill-posed problem is often addressed by classical geophysical inversion methods, which typically yield a single maximum-likelihood model that fails to capture the full range of plausible geology. The adoption of modern deep learning methods has been limited by the lack of large 3D training datasets. We address this gap with \textit{StructuralGeo}, a geological simulation engine that mimics eons of tectonic, magmatic, and sedimentary processes to generate a virtually limitless supply of realistic synthetic 3D lithological models. Using this dataset, we train both unconditional and conditional generative flow-matching models with a 3D attention U-Net architecture. The resulting foundation model can reconstruct multiple plausible 3D scenarios from surface topography and sparse borehole data, depicting structures such as layers, faults, folds, and dikes. By sampling many reconstructions from the same observations, we introduce a probabilistic framework for estimating the size and extent of subsurface features. While the realism of the output is bounded by the fidelity of the training data to true geology, this combination of simulation and generative AI functions offers a flexible prior for probabilistic modeling, regional fine-tuning, and use as an AI-based regularizer in traditional geophysical inversion workflows.