Single-shot volumetric fluorescence (SVF) imaging offers a significant advantage over traditional imaging methods that require scanning across multiple axial planes, as it can capture biological processes with high temporal resolution. The key challenges in SVF imaging include requiring sparsity constraints, eliminating depth ambiguity in the reconstruction, and maintaining high resolution across a large field of view. We introduce the QuadraPol point spread function (PSF) combined with neural fields, an approach for SVF imaging. This method utilizes a custom polarizer at the back focal plane and a polarization camera to detect fluorescence, effectively encoding the three-dimensional scene within a compact PSF without depth ambiguity. In addition, we propose a reconstruction algorithm based on the neural field technique that provides improved reconstruction quality compared with classical deconvolution methods. QuadraPol PSF, combined with neural fields, significantly reduces the acquisition time of a conventional fluorescence microscope by ∼20 times and captures a 100-mm³ cubic volume in one shot. We validate the effectiveness of both our hardware and algorithm through all-in-focus imaging of bacterial colonies on sand surfaces and visualization of plant root morphology. Our approach offers a powerful tool for advancing biological research and ecological studies.