The 21st century global competition has emphasized design of innovative products and solutions as the core competency requested today in the job market for engineers. To produce good design thinkers, design activities must be implemented in engineering curriculums, and have to start at early years. In this prospect, many leading universities have launched many interesting initiatives. These initiatives are, however, arduous for implementation in the context of universities in the developing countries due to deep-rooted local constraints, like shortage of financial and skilled human resources. Therefore, some tailored design learning initiatives, taking into account these constraints, have to be developed. In this context, a cost-effective project has been designed and implemented, in our faculty, to early introduce mechanical engineering students, in their first years, to engineering design. The proposed project was designed with respect to a proposed framework of desired engineering design competencies in conjunction with concerns for overcoming constraints and barriers of implementation context. The project encompasses two successive activities for the first and second years. The first activity plunges the students in a design thinking approach to create robotic applications using only cost-effective robotic kits. The second activity is dedicated to the design, analysis, and building of mechanical systems using only commonly used materials and cheap open hardware devices. Through this project, the students significantly improved some targeted skills as creative problem solving, communication, and teamwork. Finally, the project is thought to be valuable for all universities with similar context of limited resources.