To address the issues of inadequate accuracy and low memory efficiency in 3D point cloud registration, we propose a targeted optimization scheme (ENGO_ICP). This scheme integrates random sampling technology with an enhanced northern goshawk optimization algorithm, which is developed through multi-strategy fusion. Our objective is to improve the coarse registration phase of the iterative closest point (ICP) algorithm, which is notably sensitive to the initial transformation matrix. We partition the registration process into two main phases: coarse registration and fine registration. For coarse registration, a random sampling algorithm is employed to reduce the number of point clouds involved, thereby accelerating the speed of preliminary registration. Subsequently, we introduce an enhanced northern goshawk optimizer (ENGO) that boosts the algorithm's search capability and convergence speed by incorporating a leader-based adaptive Brownian motion strategy, nonlinear control parameters, and a leader-focused boundary control strategy. This optimizer constructs search individuals using translation and rotation transformation parameters, facilitating high-quality initial poses for the subsequent fine registration of the ICP point cloud. To validate our method's effectiveness, we conducted simulation experiments using the FGR dataset. Our method's performance is compared against classical point cloud registration algorithms, including ICP, TrICP, GWO_ICP, and NGO_ICP, using the root mean square error (RMSE) as the evaluation metric. The experimental results demonstrate superior accuracy of our proposed method.