While traditional high-fidelity methods for solving Partial Differential Equations (PDEs) are highly accurate, their computational cost in many-query scenarios has led to the rise of Scientific Machine Learning (SciML) as a promising paradigm to build data-driven surrogates that incorporate physical and mathematical knowledge. Among recent SciML architectures, Latent Dynamics Networks (LDNets) have demonstrated remarkable performance in predicting the response of spatio-temporal systems, combining Neural ODEs with reduced-order modeling. However, their application has been limited by fixed initial states. In this work, we generalize the LDNet architecture to handle variable initial conditions, broadening their applicability, and enabling the prediction of system evolution from arbitrary measured states. To achieve this, we introduce novel auto-decoding strategies to effectively represent the initial conditions within the lower-dimensional latent space. Crucially, this approach retains the encoder-free nature of the original LDNet architecture, thus preserving resolution independence and the ability to seamlessly process various data formats (e.g., images, graphs). Furthermore, we integrate meta-learning techniques by treating the initial condition as task-specific information, significantly enhancing model generalization and performance. We demonstrate the efficacy of our proposed framework across several challenging benchmarks, ranging from advection-diffusion-reaction equations to computational fluid dynamics.