Composite materials are vulnerable to impacts that may occur during their use. Such transverse loads represent a significant threat to these materials because they can cause damage that is difficult to detect. Thus, understanding the mechanical behavior of composite materials during impacts is crucial for improving their damage resistance. Therefore, this study investigates the response of two commonly used composite panels in maritime transportation—a PVC core sandwich composite and a laminated GFRP composite—under quasi-static indentation (QSI). Using numerical simulations with Abaqus/Explicit, this investigation aims to anticipate mechanical characteristics and damage patterns during low-velocity impact. Results show a strong correlation between numerical and experimental data. The force-displacement curves aid in understanding damage sequences, with predicted maximum loads at 1.43% and 6.45% accuracy for laminated and sandwich composites. Both exhibit significant damage, including permanent indentation, matrix cracks, fiber fractures, and prevalent delamination around the impact point.