The geometric processing of spaceborne synthetic aperture radar (SAR) images plays a crucial role in achieving the high-precision positioning of SAR images. Traditional SAR image geometric processing models include rigorous sensor models and rational polynomial coefficient models. However, these models are not always fully applicable to complex SAR image geometric processing scenarios. To address this issue, we propose an innovative framework for spaceborne SAR image geometric processing, aiming to realize the training of SAR image geometric processing models. The framework primarily relies on the generation of coordinate samples based on the rigorous imaging model of spaceborne SAR and utilizes a network model called the Spaceborne Synthetic Aperture Radar Coordinates Points-Radial Basis Function Neural Network (SARCoorP-RBFNet), composed of radial basis function neurons, to approximate the mapping relationship between the heterogeneous spatial coordinates and the corresponding ground coordinates. The network is trained using the generalized inverse matrix method to achieve more stable performance. The proposed method has been tested on spaceborne SAR images covering most cities in China with resolutions of 1, 3, 5, 8, and 25 m in the imaging area. The results demonstrate that SARCoorP-RBFNet achieves a large number of well-fitted heterogeneous spatial coordinate point pairs with an accuracy higher than 5% of a pixel and exhibits significant advantages in complex scenarios involving the geometric processing of multiple images.