High-quality textures are critical for realistic 3D content creation, yet existing generative methods are slow, rely on UV maps, and often fail to remain faithful to a reference image. To address these challenges, we propose a transformer-based framework that predicts a 3D texture field directly from a single image and a mesh, eliminating the need for UV mapping and differentiable rendering, and enabling faster texture generation. Our method integrates a triplane representation with depth-based backprojection losses, enabling efficient training and faster inference. Once trained, it generates high-fidelity textures in a single forward pass, requiring only 0.2s per shape. Extensive qualitative, quantitative, and user preference evaluations demonstrate that our method outperforms state-of-the-art baselines on single-image texture reconstruction in terms of both fidelity to the input image and perceptual quality, highlighting its practicality for scalable, high-quality, and controllable 3D content creation.