Conductor casing installation by self-weight and impact driving involves large deformations, strong soil-structure interaction, and transient dynamics that challenge small-strain numerical methods. We develop a 2D axisymmetric Material Point Method (MPM) model in Anura3D to simulate self-weight penetration and hammer driving of a full-scale 36 in (0.91 m) diameter, 58.8 m long conductor casing within a 30 m radius soil domain comprising four undrained soft-clay layers. The soil behavior follows an undrained Mohr-Coulomb model calibrated to site data, and an adhesive contact formulation represents the soil-casing interface. A systematic numerical study evaluates grid and particle resolution, time-step selection, damping, and time-integration schemes to achieve stable stress transfer and repeatable penetration under impact loading. The model reproduces the measured driving response up to 21 m penetration, matching field blow count per meter with 3.82% deviation. Results show that a carefully stabilized MPM workflow provides a predictive tool for offshore conductor installation in layered soft clays, reducing uncertainty in installation performance and supporting safer well foundation design