The study of parameterized dynamical systems is of paramount importance in several fields, with relevant applications in engineering, physics, and medicine. A direct investigation of their behavior for multiple parameter configurations is often computationally prohibitive, necessitating the development of suitable Reduced Order Models (ROMs). In particular, many data-driven surrogate models have recently emerged as effective strategies for approximating system dynamics in low-dimensional latent spaces, reducing computational cost while enhancing interpretability. Our investigation aims to bridge two recently proposed architectures, namely Latent Dynamics Networks (LDNets) and Graph Convolutional Autoencoders (GCA-ROMs), to accurately capture temporal evolution and handle complex and possibly varying geometries. LDNets, being meshless architectures, offer lightweight training and excellent performances but may struggle to tackle complex spatial domains. In contrast, GCA-ROMs introduce a geometric bias to help generalize across different geometries, but they usually lack causality, since time is simply considered as a parameter. To address these limitations, we adopt a mixed approach that leverages the strengths of both strategies. Similar to LDNets, we propose a two-branch architecture: the first network has a recurrent nature and models the latent dynamics of the system, while the second network, inspired by GCA-ROMs, reconstructs the full-order solution employing a graph convolutional decoder. This design enables causal modeling within an encoder-free framework, while retaining the ability to generalize across complex geometries, thus providing a flexible and expressive surrogate model. We demonstrate our approach on computational mechanics problems, featuring physical and/or dynamical parameters, and compare its performance to existing methodologies.