Single-particle cryo-electron microscopy (cryo-EM) aims to determine three-dimensional (3D) structures of biomolecular complexes from noisy two-dimensional (2D) projection images acquired at unknown orientations. The presence of pose uncertainty and continuous conformational heterogeneity makes high-resolution reconstruction challenging. Here, we investigate, in a controlled synthetic setting, whether supervised learning can map noisy cryo-EM single-particle images to atomic coordinates without pose recovery or 2D projection calculations. We propose a convolutional auto-encoder to compress particle images into their corresponding latent representations, followed by a regression network to predict 3D atomic coordinates from these image latents. We show the performance of this approach using synthetic datasets of pairs of particle images and conformational models of adenylate kinase and nucleosome core particles, generated using a realistic cryo-EM forward model based on Normal Mode Analysis for simulating dynamics. Inference yielded mean RMSDs of 2.11 [A] for all-atom models of adenylate kinase (1,656 atoms) and 0.80 [A] for the coarse-grain models of nucleosome (1,041 C-P atoms). These results indicate that compact image latents preserve pose and conformation related information sufficiently well to support atomic coordinate regression. This provides a quantitative proof-of-principle for coupling image and structure spaces toward fast estimation of conformational variability in cryo-EM.