The pursuit of self-driving networks is increasing pressure on adopting intelligent, edge-based networking services. However, deploying autonomous network models within operational and large-scale infrastructures entails substantial risks that require rigorous verification and validation procedures. In this context, the application of a Network Digital Twin (NDT) is emerging as a viable approach towards intelligent network decision-making based on high-fidelity models built upon digital representations of physical network devices (i.e., Digital Twins). In this paper, we take the first steps towards efficiently provisioning NDT models. To that end, we introduce the Digital Twin Network Provisioning Problem (DigiNet), which encompasses the optimal placement of NDT models and the efficient collection of telemetry data for synchronizing NDT models with their physical counterparts. We theoretically formalize DigiNet as a Mixed-Integer Linear Programming (MILP) model and present a polynomial-time heuristic. Our results show that DigiNet outperforms baseline approaches by up to 10x regarding the number of NDT models provisioned.