Traditional chemical analysis based on laser plasma spectroscopy (LPS) requires time-gated detectors, to avoid the initial signal from the hot plasma. These detectors are expensive and often need to be cooled and protected against vapor condensation. We suggest a low-cost setup that may replace these gated detectors, while maintaining acceptable analytical performance. The proposed setup is a result of investigation of plasma-front propagation in LPS analysis. It is known that the LPS plasma propagation is similar to the shock wave propagation after a strong explosion in the atmosphere. We found that the propagation of the plasma fits well the Sedov blast wave theory, providing a good agreement between the theoretical and experimental figures. A proper observation geometry, which is perpendicular to the plasma expansion vector, enables converting spatial to temporal resolution. We take advantage of the fact that the plasma reaches a given distance above the analyzed surface at a certain time delay. Therefore, a single optical fiber, positioned at a well-defined geometry, can provide spectral information corresponding to a certain time delay. A multifiber imaging spectrometer provides information corresponding to a series of delay times, which is adequate for analysis of a variety of matrixes. It was found that the performance of the nongated detector observing a narrow solid angle is similar to that of a gated one observing the whole plasma. For one particular example, observing the plasma from a distance of 4.5 mm is equivalent to a delay of 4 μs and integration time of 2 μs. The ratio of spectral lines of two elements was investigated using the spatially resolved (nongated) setup, and it was found that this mode is advantageous when internal calibration is applied. It was concluded that sensitive LPS analyses can be carried out by less expensive (nongated) detectors.