This research aims to develop and apply an engineering-focused STEAM program based on a project approach to examine changes in young children’s scientific inquiry ability, mathematical problem-solving ability, and creativity. A literature review and a demand survey on the theme of “cars” were conducted in P public kindergarten located in S-district, I city for eight weeks on 21 five-year-old children. The data were analyzed qualitatively, and to examine the changes from the program, the quantitative observation checklist data were analyzed by conducting repeated measures ANOVA. This program combined the project approach model and the early childhood engineering design process model to the teaching-learning stages: the exploration stage of topic selection and grasping prior experience, the design stage of problem solution exploration, the trial stage, the solution stage, and the problem-solving process sharing stage. Based on the analysis of collected data, the exploring, operating, and constructing the car and the opportunity to transform it into a new structure brought positive changes in young children’s scientific inquiry ability, mathematical problem-solving ability, and creativity. These results suggest the engineering-focused STEAM program as one of the models for fostering creative-convergence talents and provides data for developing a curriculum to operate an engineering-focused STEAM program in early childhood care and education.