The spread of invasive species poses a major ecological and economical threat. Consequently there are ongoing efforts to develop a generalizable mechanism to predict establishment success of non-native species. One proposed mechanism to predict establishment success is propagule pressure, which is defined as the number of individuals introduced at a given time. Although some studies have demonstrated a positive correlation between propagule pressure and establishment success, others have not, and the effect of propagule pressure on establishment success remains unclear. To address this challenge, a strain of bacteria engineered with an Allee effect, a growth dynamic that is often associated with establishing species, was used. The timing between successive introduction events that resulted in establishment success was measured. It was observed that if the time between two introduction events was sufficiently long, growth did not occur. By manipulating the growth rate of the bacteria, it was shown that that the minimal time between the two introduction events that resulted in growth was constrained as growth rate decreased. Moreover, it was concluded that asymmetry in the density of bacteria introduced in the introduction events increased the maximum time between introduction events that resulted in growth. These results help to remedy conflicting data in the literature by identifying conditions where propagule pressure has, and does not have, a positive impact on establishment success. These findings can have major implications in understanding and predicting the unique population dynamics of invasive species.