Motivation: Structural information of macromolecular complexes provides key insights into the way they carry out their biological functions. The reconstruction process leading to the final 3D map requires an approximate initial model. Generation of an initial model is still an open and challenging problem in single-particle analysis. Results: We present a fast and efficient approach to obtain a reliable, low-resolution estimation of the 3D structure of a macromolecule, without any a priori knowledge, addressing the well-known issue of initial volume estimation in the field of single-particle analysis. The input of the algorithm is a set of class average images obtained from individual projections of a biological object at random and unknown orientations by transmission electron microscopy micrographs. The proposed method is based on an initial non-lineal dimensionality reduction approach, which allows to automatically selecting representative small sets of class average images capturing the most of the structural information of the particle under study. These reduced sets are then used to generate volumes from random orientation assignments. The best volume is determined from these guesses using a random sample consensus (RANSAC) approach. We have tested our proposed algorithm, which we will term 3D-RANSAC, with simulated and experimental data, obtaining satisfactory results under the low signal-to-noise conditions typical of cryo-electron microscopy.