Phase-field simulations of liquid metal dealloying (LMD) can capture complex microstructural evolutions but can be prohibitively expensive for large domains and long time horizons. In this presentation, we introduce a fully convolutional, conditionally parameterized U-Net surrogate designed to extrapolate far beyond its training data in both space and time. The architecture integrates convolutional self-attention and physically informed padding methods to maintain accuracy in extrapolation regimes. The algorithm allows conditioning on simulation parameters allows for flexible time-step skipping and adaptation to varying alloy compositions. To remove the need for costly solver-based initialization, we couple the surrogate with a conditional diffusion model that generates synthetic, physically consistent initial conditions. The surrogate model is trained using simulations generated over small domain sizes and short time spans. By taking advantage of the convolutional nature of U-Nets, we are able to run and extrapolate surrogate simulations for longer time horizons than what would be achievable with classic numerical solvers. Across multiple alloy compositions, the framework is able to reproduce the LMD physics accurately. It predicts key quantities of interest and spatial statistics with relative errors typically below 5\% in the training regime and under 15\% during large-scale, long time-horizon extrapolations. Our framework can also deliver speed-ups of up to $36,000\times$, bringing the time to run weeks-long simulations down to seconds. This work is a first stepping stone towards high-fidelity extrapolation in both space and time of phase-field simulation for LMD.