Neural rendering with Gaussian splatting has advanced novel view synthesis, and most methods reconstruct surfaces via post-hoc mesh extraction. However, existing methods suffer from two limitations: (i) inaccurate geometry in texture-less indoor regions, and (ii) the decoupling of mesh extraction from optimization, thereby missing the opportunity to leverage mesh geometry to guide splat optimization. In this paper, we present OMeGa, an end-to-end framework that jointly optimizes an explicit triangle mesh and 2D Gaussian splats via a flexible binding strategy, where spatial attributes of Gaussian Splats are expressed in the mesh frame and texture attributes are retained on splats. To further improve reconstruction accuracy, we integrate mesh constraints and monocular normal supervision into the optimization, thereby regularizing geometry learning. In addition, we propose a heuristic, iterative mesh-refinement strategy that splits high-error faces and prunes unreliable ones to further improve the detail and accuracy of the reconstructed mesh. OMeGa achieves state-of-the-art performance on challenging indoor reconstruction benchmarks, reducing Chamfer-$L_1$ by 47.3\% over the 2DGS baseline while maintaining competitive novel-view rendering quality. The experimental results demonstrate that OMeGa effectively addresses prior limitations in indoor texture-less reconstruction.