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The present study evaluates the performance of two numerical approaches in estimating non-equilibrium scour patterns around a non-slender square structure subjected to a transient wave, by comparing numerical findings with experimental data. This study also investigates the impact of the structure’s positioning on bed evolution, analyzing configurations where the structure is either attached to the sidewall or positioned at the centerline of the wave flume. The first numerical method treats sediment particles as a distinct continuum phase, directly solving the continuity and momentum equations for both sediment and fluid phases. The second method estimates sediment transport using the quadratic law of bottom shear stress, yielding robust predictions of bed evolution through meticulous calibration and validation. The findings reveal that both methods underestimate vortex-induced near-bed vertical velocities. Deposits formed along vortex trajectories are overestimated by the first method, while the second method satisfactorily predicts the bed evolution beneath these paths. Scour holes caused by wave impingement tend to backfill as the flow intensity diminishes. The second method cannot sufficiently capture this backfilling, whereas the first method adequately reflects the phenomenon. Overall, this study highlights significant variations in the predictive capabilities of both methods in regard to the evolution of non-equilibrium scour at low Keulegan–Carpenter numbers.