Despite recent rapid developments in computer programs used to improve buildings construction sector cost estimation techniques, costing models utilizable in a building construction project’s early planning stages remain scarce due to the lack of a simplified, integrated method that can operate with the limited data available. This research aimed to help buildings construction project stakeholders in Iraq to improve the accuracy of preliminary buildings project cost estimations based on the initial information available and historical buildings project data to evaluate a future project’s feasibility. A literature review of topics related to preliminary cost estimation, particularly buildings projects and factors affecting their cost, informed development of an integrated mathematical model based on a support vector machine to facilitate preliminary cost estimation during early buildings construction project planning utilizing relevant factors from both old and new projects (i.e., total floor area of buildings, construction duration, total number of floors, average floor height, location index, project quality standards, project complexity, and facilities provision). To enhance accuracy, the final cost forecasting model was modified using an inflation rate impact scenario to account for any future economic effects on anticipated building costs. This study concluded that the dominant factors behind cost variations between similar projects over different periods, and thus the primary factors for building cost estimation, are building area, average floor height, and number of floors. Thus, this study contributes to enhancing best practice in cost estimating for building construction projects in the pre-design, early planning phase, enabling decision makers to plan alternative options to enhance decisions on feasibility within the project’s constraints. Novelty arises from the features of the input factors used for the developed model to determine the preliminary budget required in the early planning stage taking into account construction sector inflation values for the following period.