Computational thinking (CT) is regarded as a crucial skill that every 21st-century citizen should possess. Therefore, the development of this skill should start at preschool age. According to the existing literature, educational robotics may be a vehicle for CT enhancement. However, despite the increased interest of researchers in implementing programs that contribute to the development of computational thinking in educational environments, empirical research in the field of preschool education is limited. The aim of the pilot study was to examine the potential role of educational robotics in fostering the development of CT among preschool-aged children and the gender and age effect. This study used structured problem-based robotic activities developmentally appropriate for 4–6 aged preschoolers to cultivate CT while programming the robot Beebot. Activities implementing young children in simple and complex algorithms, decomposition, pattern recognition, and debugging were used. Results indicated that a robotic course could promote overall CT development in kindergarten settings. Gender and age factors did not affect kindergartener’s CT scores. Researchers in the field of CT may benefit from this work regarding the best tools for CT development.