Strong-field-induced Coulomb explosion imaging (CEI) has emerged as a powerful tool for probing molecular geometry in momentum-space. However, reconstructing the original three-dimensional structure of polyatomic molecules remains a long-standing challenge due to the inherent complexity of multidimensional inversion. Here, we introduce a deep neural framework that bridges this gap by directly recovering position-space molecular structures from Coulomb explosion momentum patterns. Our approach combines CEI simulations with a neural network trained to establish the mapping between momentum-space Newton plots and real-space geometries. The trained model demonstrates high fidelity in reconstructing the structure of CHF${}_3$ from experimental CEI data. This generalizable framework can not only be extended to other molecular systems but also opens avenues for time-resolved structural analysis of molecular dynamics.