Intraoperative 2D/3D registration, which aligns preoperative CT scans with intraoperative X-ray images, is critical for surgical navigation. However, existing methods require extensive preoperative training (several hours), making them unsuitable for emergency surgeries where minutes significantly impact patient outcomes. We present GaussianReg, a novel registration framework that achieves clinically acceptable accuracy within minutes of preprocessing. Unlike prior approaches that learn primarily from 2D projections, we explicitly utilize 3D information by representing CT volumes as sparse Gaussian primitives and propose an innovative ray-based registration approach. These primitives emit rays toward potential camera positions, creating a hypothesis space of viewpoints. The registration problem then reduces to identifying rays that best match the target X-ray through our cross-modality attention mechanism. We further introduce canonical ellipsoid ray parameterization for stable optimization, bipartite matching-based patch aggregation for computational efficiency, and network pruning to accelerate training. Extensive experiments demonstrate that GaussianReg achieves 10mm-level accuracy with only 10 minutes of training, compared to hours required by existing methods. Our approach thus offers a promising solution for emergency surgical scenarios where rapid adaptation to patient-specific anatomy is critical.