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Reconstructing continuous surfaces from unoriented and unordered 3D points is a fundamental challenge in computer vision and graphics. Recent advancements address this problem by training neural signed distance functions to pull 3D location queries to their closest points on a surface, following the predicted signed distances and the analytical gradients computed by the network. In this paper, we introduce NumGrad-Pull, leveraging the representation capability of tri-plane structures to accelerate the learning of signed distance functions and enhance the fidelity of local details in surface reconstruction. To further improve the training stability of grid-based tri-planes, we propose to exploit numerical gradients, replacing conventional analytical computations. Additionally, we present a progressive plane expansion strategy to facilitate faster signed distance function convergence and design a data sampling strategy to mitigate reconstruction artifacts. These components are synergistically integrated into a unified tri-plane-based pulling framework, in which numerical gradients, progressive expansion, and complementary sampling jointly address the locality and sparsity challenges of learning SDFs from unoriented point clouds. Our extensive experiments across a variety of benchmarks demonstrate the effectiveness and robustness of our approach. Codes are available at: https://github.com/cuiruikai/numgrad-pull.