Additive manufacturing with cement-based materials, and in particular 3D Concrete Printing (3DCP), has attracted growing attention to enhance productivity, structural performance, and architectural freedom in the construction industry. By extruding a cementitious mortar through a digitally controlled nozzle, 3DCP enables the layer-by-layer fabrication of structural elements without formwork, allowing the realization of topologically optimized geometries while reducing material waste, construction time, and environmental impact. Numerical modelling plays a crucial role in improving understanding, prediction, and control of 3DCP processes. However, modelling 3DCP is inherently challenging due to the coexistence of multiple physical phenomena across different spatial and temporal scales, including non-Newtonian rheology, free-surface flow, and large deformations. High-fidelity approaches based on continuum mechanics, and in particular the Particle Finite Element Method (PFEM), have demonstrated excellent accuracy in predicting filament geometry and extrusion physics. Nevertheless, their high computational cost severely limits their applicability to large-scale simulations and design-oriented use Nevertheless, their high computational cost severely limits their applicability to large-scale simulations and design-oriented use. To overcome this issue, recent research has explored either improving solver efficiency or deriving simplified machine learning-based design tools for the fast prediction of selected features (e.g., cross-sectional shape). In this work, we propose a data-driven surrogate modelling approach for 3DCP based on NeuralPFEM, a recently introduced framework for free-surface flow simulation. NeuralPFEM preserves the mesh management, remeshing strategies, and overall structure of PFEM, while replacing the finite element time integration with an autoregressive neural network. This enables accurate prediction of velocity and pressure fields at a fraction of the computational cost of the full-order PFEM model. The framework is extended to address challenges specific to 3DCP, including the continuous addition of nodes associated with material extrusion and layer deposition. The surrogate is trained on a dataset of high-fidelity PFEM simulations and evaluated against reference results. NeuralPFEM accurately reproduces the entire deposition process, including free-surface evolution, while achieving substantial computational speedups.