Many engineering problems involve modeling of structural dynamics subjected to contact. Simulations of such problems are more expensive since they require determination of the contact region, consideration of non-penetration conditions, and calculation of contact pressures. Numerical experiments for the analysis and optimization of systems with many degrees of freedom can be very time-consuming in this case. To accelerate the simulations, there is a need to develop methods to find smaller surrogate models that can accurately approximate the contact behavior of the full-order model. Moreover, since access to the actual model is very limited in well-established commercial contact simulation software, we aim to obtain the reduced-order model in a data-driven manner. \\ In this work, we consider node-to-node contact problems solved by adjoint methods. Inspired by the successful reduction of such problems using the intrusive Arnoldi process in combination with the classical Craig-Bampton substructuring method, we propose to incorporate the latter approach into operator-inference-based optimization. The novel methodology provides the reduced system matrices and the coupling of the contact and interior nodes. \\ The particular advantage of the proposed method is that only the solution snapshots of a simulation without active contact (contact-free simulations) and the maximum set of possible contact nodes are required. Therefore, the proposed approach allows us to save resources in the offline snapshot generation phase. In addition, we preserve the characteristic properties of the inferred matrices, such as symmetry and positive definiteness, by adding constraints to the operator inference least-squares problem. The resulting dual system, which forms a linear complementarity problem, is well-defined and can be solved efficiently using methods such as Lemke’s algorithm. The performance of the proposed method is validated on three-dimensional finite element models. Different aspects of substructuring and data generation that affect the accuracy of the results are discussed.