We systematically investigate the avalanche-to-streamer transition (AST) over a wide range of pressures and homogenous background electric fields and for a comprehensive list of gases, namely pure nitrogen, carbon dioxide, oxygen, argon, sulfur hexafluoride and synthetic air. The discharge starts from an initial seed electron and is temporally followed from the avalanche regime, through the first significant distortion of the background field and the subsequent increasing deviation from the Gaussian electron density profile, up to the occurrence of runaway electrons accompanied by the sudden and dramatic increase of electron energy and electron number multiplication. We detect weak influence of the background electric field value and the gas composition, but strong influence of the gas density on the electron number at which the transition occurs. The simulations are performed by means of a fully-interacting particle simulation program that combines a particle-in-cell/Monte Carlo collision model (PIC/MCC) with a three-dimensional Poisson solver in order to account for the space charge generated by the electrons and ions. The freely-available program is based on the METHES code and is universally applicable to arbitrary gas mixtures with complete cross section sets.