Cavity exploration is an important task for optical remote sensing that finds application in many fields, such as the assessment of disaster areas or the evaluation of subsurface cavities in terrestrial and extraterrestrial scenarios. In our work, we use single photon-counting avalanche diode cameras to record temporal signatures in the picosecond time domain and to exploit the impulse response of cavities. When illuminated with a short optical pulse, the photons are reflected several times inside the cavity before exiting it and being detected. In our datasets, we observe several intensity modulations correlated to specific optical paths with different numbers of reflections inside the cavity. We developed an analysis model based on simulation of the radiant transfer that provides a quick rough estimate of the cavity dimensions without costly measurements or computational reconstruction. Specifically, we developed a spherical model and a hemispherical model that can be used to estimate the cavity dimensions (diameter or height). Finally, we present experimental studies of eight different cavities with different dimensions, shapes, and surface materials. Our evaluations show that we can apply our analytical models to signatures of different cavities, which gives us an initial estimate of the cavity sizes before a detailed mapping is carried out.