Object detection in satellite-borne Synthetic Aperture Radar (SAR) imagery holds immense potential in tasks such as urban monitoring and disaster response. However, the inherent complexities of SAR data and the scarcity of annotations present significant challenges in the advancement of object detection in this domain. Notably, the detection of small objects in satellite-borne SAR images poses a particularly intricate problem, because of the technology's relatively low spatial resolution and inherent noise. Furthermore, the lack of large labelled SAR datasets hinders the development of supervised deep learning-based object detection models. In this paper, we introduce TRANSAR, a novel self-supervised end-to-end vision transformer-based SAR object detection model that incorporates masked image pre-training on an unlabeled SAR image dataset that spans more than $25,700$ km\textsuperscript{2} ground area. Unlike traditional object detection formulation, our approach capitalises on auxiliary binary semantic segmentation, designed to segregate objects of interest during the post-tuning, especially the smaller ones, from the background. In addition, to address the innate class imbalance due to the disproportion of the object to the image size, we introduce an adaptive sampling scheduler that dynamically adjusts the target class distribution during training based on curriculum learning and model feedback. This approach allows us to outperform conventional supervised architecture such as DeepLabv3 or UNet, and state-of-the-art self-supervised learning-based arhitectures such as DPT, SegFormer or UperNet, as shown by extensive evaluations on benchmark SAR datasets.