Manual handling and packing of thin metal plates remains a labor-intensive operation in the automotive manufacturing sector, frequently requiring multiple operators and resulting in limited productivity, reduced process repeatability, and ergonomic constraints. This paper presents a preliminary virtual and experimental proof of concept for the automation of such a packing task using a delta robot, motivated by a representative industrial scenario involving automotive heat exchanger plates. The proposed study adopts an intentionally simplified problem formulation to support early-stage feasibility assessment and system design. In the considered scenario, the approximate initial position of each plate is assumed to be known at the moment it is released onto a tray, allowing the study to focus on the robotic packing stage rather than on part detection. A virtual robotic packing cell is developed using MATLAB-based simulation tools, with particular emphasis on workspace definition, packing layout design, and end-effector selection. The target placement positions inside the packing tray are fully defined in the robot coordinate system, enabling the analysis of reachability, packing density, and achievable cycle times without introducing additional complexity related to sensing or perception. A set of performance-oriented indicators is defined and evaluated in simulation, including workspace utilization, throughput, and packing efficiency. Based on the virtual results, a simplified experimental demonstrator is implemented to provide initial validation of the proposed concept, using representative plate geometries and a programmed packing sequence. This experimental stage is not intended as a full industrial validation, but rather as a functional verification of the feasibility of delta robot-based packing under controlled conditions. By deliberately limiting the system scope, the study establishes a baseline for robotic packing performance and provides a structured foundation for subsequent research, which will address more realistic industrial conditions such as imprecise plate positioning, surface contamination, vision-based perception, robot–sensor calibration, and scenarios involving multiple plates simultaneously.