It is important to estimate an accurate signed distance function (SDF) from a point cloud in many computer vision applications. The latest methods learn neural SDFs using either a data-driven based or an overfitting-based strategy. However, these two kinds of methods are with either poor generalization or slow convergence, which limits their capability under challenging scenarios like highly noisy point clouds. To resolve this issue, we propose a method to prompt pros of both data-driven based and overfitting-based methods for better generalization, faster inference, and higher accuracy in learning neural SDFs. We introduce a novel statistical reasoning algorithm in local regions which is able to finetune data-driven based priors without signed distance supervision, clean point cloud, or point normals. This helps our method start with a good initialization, and converge to a minimum in a much faster way. Our numerical and visual comparisons with the stat-of-the-art methods show our superiority over these methods in surface reconstruction and point cloud denoising on widely used shape and scene benchmarks. The code is available at https://github.com/chenchao15/LocalN2NM.