We show that individual (single-epoch) spectra of active galactic nuclei (AGNs) can constrain some of the geometry and dynamics of the AGN broad line region. Studies of the cosmic influence of supermassive black holes are limited by the current large uncertainties in the determination of black hole masses. One dominant limitation is the unknown geometry, dynamics, and line-of-sight inclination of the broad line region, used to probe the central black hole mass. Recent progress has been made to constrain the spatial and kinematic structure of the broad line region using dynamical modelling of AGN monitoring data and an underlying physical model for the broad line region. In this work we test the ability of a modified version of this dynamical modelling code to constrain the broad line region structure using single-epoch spectra. We test our modelling code on single-epoch spectra of nearby Arp 151 by comparing our results with those obtained with monitoring data of this same object. We find that a significant fraction of the broad line region parameters can indeed be adequately constrained, with uncertainties that are comparable to, or at most a factor of approximately a few higher than those obtained from modelling of monitoring data. Considering the wealth of available single-epoch spectroscopic observations, this method is promising for establishing the overall AGN population trends in the geometry and dynamics of the broad line region. This method can be applied to spectra of AGNs at low and high redshift making it valuable for studies of cosmological black hole and AGN evolution.