Transient stability prediction is critically essential to the fast online assessment and maintaining the stable operation in power systems. The wide deployment of phasor measurement units (PMUs) promotes the development of data-driven approaches for transient stability assessment. This paper proposes the temporal and topological embedding deep neural network (TTEDNN) model to forecast transient stability with the early transient dynamics. The TTEDNN model can accurately and efficiently predict the transient stability by extracting the temporal and topological features from the time-series data of the early transient dynamics. The grid-informed adjacency matrix is used to incorporate the power grid structural and electrical parameter information. The transient dynamics simulation environments under the single-node and multiple-node perturbations are used to test the performance of the TTEDNN model for the IEEE 39-bus and IEEE 118-bus power systems. The results show that the TTEDNN model has the best and most robust prediction performance. Furthermore, the TTEDNN model also demonstrates the transfer capability to predict the transient stability in the more complicated transient dynamics simulation environments.