In this paper we propose a new approach to incrementally initialize a manifold surface for automatic 3D reconstruction from images. More precisely we focus on the automatic initialization of a 3D mesh as close as possible to the final solution; indeed many approaches require a good initial solution for further refinement via multi-view stereo techniques. Our novel algorithm automatically estimates an initial manifold mesh for surface evolving multi-view stereo algorithms, where the manifold property needs to be enforced. It bootstraps from 3D points extracted via Structure from Motion, then iterates between a state-of-the-art manifold reconstruction step and a novel mesh sweeping algorithm that looks for new 3D points in the neighborhood of the reconstructed manifold to be added in the manifold reconstruction. The experimental results show quantitatively that the mesh sweeping improves the resolution and the accuracy of the manifold reconstruction, allowing a better convergence of state-of-the-art surface evolution multi-view stereo algorithms.