Synthetic Aperture Radar (SAR) object detection faces significant challenges from speckle noise, small target ambiguities, and on-board computational constraints. While existing approaches predominantly focus on SAR-specific architectural modifications, this paper explores the application of the existing lightweight object detector, i.e., YOLOv10, for SAR object detection and enhances its performance through Neural Architecture Search (NAS). Specifically, we employ NAS to systematically optimize the network structure, especially focusing on the backbone architecture search. By constructing an extensive search space and leveraging evolutionary search, our method identifies a favorable architecture that balances accuracy, parameter efficiency, and computational cost. Notably, this work introduces NAS to SAR object detection for the first time. The experimental results on the large-scale SARDet-100K dataset demonstrate that our optimized model outperforms existing SAR detection methods, achieving superior detection accuracy while maintaining lower computational overhead. We hope this work offers a novel perspective on leveraging NAS for real-world applications.