Accurately estimating the cost of software development is crucial for effective project planning and resource allocation. However, traditional cost estimation methods rely heavily on expert judgment and historical data, which can be time consuming and prone to errors. This study suggests a learning-based cost estimation model that leverages relational databases to improve accuracy. The proposed approach estimates project cost based on the effort required to complete software development, which is a key driver of the project cost. The proposed model is designed to address the challenges posed by the variability in open-source development, including variable team sizes, working hours, and expertise. The study collects and pre-processes data from open-source platforms and selects cost drivers and metrics based on logical rules and SQL queries. Moreover, we propose an optimized Artificial Neural Network (ANN) with augmented topology to automate the selection of neuron units, layers, and adjustment of learnable parameters according to the input variables. The proposed model is evaluated on a 100 open-source software repositories dataset and demonstrates its effectiveness in accurately estimating development cost. The system is implemented using Python and evaluated using performance parameters such as MSE, RMSE, MAE, and MMRE. Results indicate that our proposed model offers a more accurate and efficient approach to software cost estimation, especially for freelancers and outsourcing firms. The proposed model has the potential to save time and resources and improve the reliability and accuracy of software cost estimation.