Start-ups require a coherent strategy of resource allocation to grow and survive as they encounter environmental uncertainties and resource limitations when they enter foreign markets. Hence, to attain sustainable growth, entrepreneurs can adopt the “growth engines” strategy defined by the lean start-up method. To cope with the complexity of growth decisions in start-ups, and to analyse engines’ feedback loops, system dynamics (SD) simulation methodology has been used through causal relationships between the main variables and the developing stock-flow diagram. In addition to the lean approach, a real-world case study was also applied for model simulation, and an optimum policy was provided for each proposed scenario. Five different scenarios and five practical policies, each related to a specific growth engine, were simulated. Simulation results were discussed to facilitate decision on which engine must be prioritised in particular environmental conditions, and when making a pivot decision is necessary. Ideally, comparing simulation results under different scenarios to the base run revealed a substantial increase in the customer lifetime value resulting from focusing on the sticky engine with no increased customer attraction. Finally, this study highlighted the importance of selecting only one main strategy from customer acquisition and customer retention at a time and tried to attain the optimal value of customers over the long term. Moreover, research findings may be also useful for start-up executives seeking business growth by adopting correct decisions on how to obtain optimal results under conditions of extreme uncertainty.