The search for weakly interacting massive particles (WIMPs) remains a central goal of the High Luminosity Large Hadron Collider (HL-LHC). In this work, we explore radiative neutralino decays within the framework of the $Z_3$-symmetric Next-to-Minimal Supersymmetric Standard Model (NSSM), focusing on scenarios where the lightest supersymmetric particle (LSP) is a singlino-dominated neutralino. In this setting, the correct dark matter relic density can be achieved through coannihilation with higgsino- or bino-like states, while also evading current direct detection bounds via blind spot conditions. In particular, in singlino–higgsino coannihilation scenarios, radiative decays of the heavier neutralinos into the singlino LSP and a photon can be significantly enhanced, motivating dedicated searches at the HL-LHC. These decays yield challenging final states characterized by at least one soft photon, a lepton, and a large missing transverse energy signature, enhanced by a hard initial-state radiation jet. We employ a Machine Learning (ML)– based analysis that enhances sensitivity to these faint signatures, providing a robust, data-driven complement to conventional search strategies in the exploration of new physics scenarios. Our results demonstrate that the use of ML classifiers significantly improves the discrimination power against Standard Model (SM) backgrounds, offering promising discovery potential in this well-motivated dark matter (DM) scenario.