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Three-dimensional non-local thermodynamic equilibrium (3D NLTE) radiative transfer is essential for interpreting modern solar and stellar atmosphere simulations, but conventional codes such as Multi3D remain computationally expensive for large snapshot sequences and repeated spectral synthesis. We present a Fourier Neural Operator-based framework designed as a geometry-aware surrogate to calculate 3D NLTE population calculations from 3D stellar atmospheres. Unlike earlier machine-learning surrogates that use local neighborhoods to predict a center voxel or center column, our framework learns an operator from the full 3D atmospheric state to the full 3D NLTE departure coefficient volume. The model is therefore not a column-wise correction scheme, but a volumetric predictor trained directly on whole-atmosphere input-output fields. During training, it sees the surrounding atmospheric structure as part of the target itself, rather than using neighboring columns only as auxiliary context. The inputs include temperature, density, electron density, and velocity components, while the targets are departure coefficients for selected atomic levels. The architecture combines horizontal spectral operators with a coordinate-conditioned vertical branch, enabling it to capture lateral radiative coupling and depth-dependent NLTE structure. Crucially, the model explicitly incorporates physical horizontal grid spacings dx and dy, and accepts a native z_scale, including arbitrary non-uniform vertical grids. It is therefore not tied to fixed pixel spacing, a uniform depth index, or a remapped common vertical coordinate. This makes the framework a true volumetric surrogate for Multi3D: it preserves global atmospheric context, supports native simulation geometry, and outputs complete 3D departure coefficient cubes for downstream spectral synthesis.