In this paper, we propose a novel method to make distance predictions in real-world social networks. As predicting missing distances is a difficult problem, we take a two-stage approach. Structural parameters for families of synthetic networks are first estimated from a small set of measurements of a real-world network and these synthetic networks are then used to pre-train the predictive neural networks. Since our model first searches for the most suitable synthetic graph parameters which can be used as an "oracle" to create arbitrarily large training data sets, we call our approach "Oracle Search Pre-training" (OSP). For example, many real-world networks exhibit a Power law structure in their node degree distribution, so a Power law model can provide a foundation for the desired oracle to generate synthetic pre-training networks, if the appropriate Power law graph parameters can be estimated. Accordingly, we conduct experiments on real-world Facebook, Email, and Train Bombing networks and show that OSP outperforms models without pre-training, models pre-trained with inaccurate parameters, and other distance prediction schemes such as Low-rank Matrix Completion. In particular, we achieve a prediction error of less than one hop with only 1% of sampled distances from the social network. OSP can be easily extended to other domains such as random networks by choosing an appropriate model to generate synthetic training data, and therefore promises to impact many different network learning problems.