Electromagnetic Inverse Scattering Problems (EISP) seek to reconstruct relative permittivity from scattered fields and are fundamental to applications like medical imaging. This inverse process is inherently ill-posed and highly nonlinear, making it particularly challenging, especially under sparse transmitter setups, e.g., with only one transmitter. While recent machine learning-based approaches have shown promising results, they often rely on time-consuming, case-specific optimization and perform poorly under sparse transmitter setups. To address these limitations, we revisit EISP from a data-driven perspective. The scarcity of transmitters leads to an insufficient amount of measured data, which fails to capture adequate physical information for stable inversion. Accordingly, we propose a fully end-to-end and data-driven framework that predicts the relative permittivity of scatterers from measured fields, leveraging data distribution priors to compensate for the incomplete information from sparse measurements. This design enables data-driven training and feed-forward prediction of relative permittivity while maintaining strong robustness to transmitter sparsity. Extensive experiments show that our method outperforms state-of-the-art approaches in reconstruction accuracy and robustness. Notably, we demonstrate, for the first time, high-quality reconstruction from a single transmitter. This work advances practical electromagnetic imaging by providing a new, cost-effective paradigm to inverse scattering. Code and models are released at https://gomenei.github.io/SingleTX-EISP/.