Gene regulatory network (GRN) inference can now take advantage of powerful machine learning algorithms to complement traditional experimental methods in building gene networks. However, the dynamical nature of embryonic development-representing the time-dependent interactions between thousands of transcription factors, signaling molecules, and effector genes-is one of the most challenging arenas for GRN prediction. In this work, we show that successful GRN predictions for a developmental network from gene expression data alone can be obtained with the Priors Enriched Absent Knowledge (PEAK) network inference algorithm. PEAK is a noise-robust method that models gene expression dynamics via ordinary differential equations and selects the best network based on information-theoretic criteria coupled with the machine learning algorithm Elastic Net. We test our GRN prediction methodology using two gene expression datasets for the purple sea urchin, Stronglyocentrotus purpuratus, and cross-check our results against existing GRN models that have been constructed and validated by over 30 years of experimental results. Our results find a remarkably high degree of sensitivity in identifying known gene interactions in the network (maximum 81.58%). We also generate novel predictions for interactions that have not yet been described, which provide a resource for researchers to use to further complete the sea urchin GRN. Published ChIPseq data and spatial co-expression analysis further support a subset of the top novel predictions. We conclude that GRN predictions that match known gene interactions can be produced using gene expression data alone from developmental time series experiments.