Precise control of material extrusion and structural build-up is critical for the advancement of 3D Concrete Printing (3DCP). This study presents a systematic numerical investigation into the screw extrusion process and the time-dependent hardening behavior of fresh concrete using the Discrete Element Method (DEM). A calibrated viscoelastic liquid bridge model was employed to capture the complex granular dynamics of the cementitious material. Regarding the screw extrusion process, the influence of key operational parameters (e.g., printing speed, screw rotation) and nozzle geometry on filament morphology and internal flow characteristics was analyzed. The study reveals that nozzle diameter is the dominant factor governing cross-sectional geometry and internal densification. Furthermore, the analysis of continuous fields, including velocity and von Mises stress, highlighted the mechanisms behind material "faulting" and stress concentration within the nozzle. Additionally, the study addresses the challenge of simulating time-dependent hardening. By dynamically adjusting the microscopic surface tension parameter within the DEM model, the transition from a fluid-like state to a solid-like state was effectively replicated. Simulations of multi-layer printing demonstrate the critical role of hardening rates in balancing extrudability and buildability. Results indicate that a properly tailored hardening rate significantly suppresses bottom-layer deformation and enhances geometric fidelity. This research provides valuable theoretical insights and quantitative guidance for optimizing nozzle design and process parameters in practical 3DCP applications.