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This work investigates how particle geometry and boundary conditions govern packing density and accessible surface area in randomly organized packed beds. We employ a superellipsoid parameterization to represent non-spherical shapes by aspect ratio (α), oblateness (β), and corner/edge sharpness (p₀, p₁). Rigid-body simulations, validated via computed tomography, were conducted under varying container-to-particle diameter ratios and particle counts. Four key metrics were systematically analyzed: packing density (PD), the total surface-to-volume ratio (SVtotal), the effective (available) surface-to-volume ratio (SVeff), and the fraction of surface area lost to inter-particle contact (SR). Results indicate that PD is primarily controlled by boundary effects, with smaller particles and higher particle counts producing denser configurations. In contrast, α and β strongly influence SVeff, as flatter, elongated particles afford higher surface area but reduce packing efficiency. Sharper edges amplify SVtotal while also raising SR, underscoring the trade-off between maximizing surface exposure and limiting contact-induced surface loss. An automated machine learning approach significantly outperforms linear regression in capturing these non-linear interactions, offering improved predictive accuracy. These findings clarify fundamental trade-offs for optimizing packed bed systems, balancing shape-driven surface benefits with boundary-driven packing constraints, and provide actionable design suggestions for applications such as thermal energy storage, catalytic reactors, and filtration.