Molecular dynamics simulations play a crucial role in scientific research. Yet their computational cost often limits the timescales and system sizes that can be explored. Most data-driven efforts have focused on reducing the computational cost of the accurate interatomic forces required to solve the equations of motion. However, despite their success, these machine-learning interatomic potentials are still bound to small time steps. In this work, we introduce TrajCast, a transferable and data-efficient framework based on autoregressive equivariant message-passing networks, that directly updates the atomic positions and velocities, lifting the constraints imposed by traditional numerical integration. We benchmark our framework across various systems, including a small molecule, crystalline material and bulk liquid, demonstrating excellent agreement with reference molecular dynamics simulations for structural, dynamical and energetic properties. Moreover, we show that TrajCast can generalize in a zero-shot manner to unseen regions of phase space, producing physically meaningful ensembles in metastable equilibrium and out-of-equilibrium regimes beyond the training data, without compromising accuracy. Depending on the system, TrajCast allows for forecast intervals up to 30× larger than traditional MD time steps, generating over 15 ns of trajectory data per day for a solid with more than 4,000 atoms. By enabling efficient, large-scale simulations over extended timescales, TrajCast can accelerate materials discovery and explore physical phenomena beyond the reach of traditional simulations and experiments. Thiemann et al. introduce TrajCast, a neural network that bypasses force calculations to directly predict atomic trajectories, enabling time steps up to 30 times longer while accurately reproducing physical properties of molecules and materials.