We present an initial assessment of using tomography on single-spacecraft images to reconstruct 3D X-ray emissions from the Earth’s magnetosheath. 3D structures in the Earth’s magnetosphere have been studied using superposed epoch techniques with single-point single-spacecraft observations. They have yielded great insights, but some studies are observation starved, particularly for infrequent solar wind conditions. Global imaging data have provided more insight about these structures, but are 2D projections of 3D structures. We explore the use of tomographic reconstruction techniques to understand what can be extracted from global images from a single spacecraft. The Solar wind Magnetosphere Ionosphere Link Explorer (SMILE) mission, due to launch in 2024 on a 3-year mission, will carry a soft X-ray imager which will capture emissions from portions of the magnetosheath and upstream solar wind. We already demonstrated that the 3D shape of the magnetopause and the bow shock can be extracted from such images with suitable assumptions. The next step is to examine whether full 3D reconstructions of the emissions are possible. We explore the limited range of viewing angles, which affect the accuracy of the reconstructions and introduce artifacts in some cases, and the low count-rates in the images which introduce noise in the reconstructions which must be filtered out. Despite these limitations we show that it is possible to reconstruct some aspects of the magnetosheath global morphology using single-spacecraft soft X-ray imaging. Plans for similar missions which overlap with SMILE, open the possibility of multi-spacecraft tomography, to be addressed in a separate paper.