Plato\'s Republic, Einstein\'s Theory of relativity, Vilvadi\'s Four Seasons are all remarkable examples of humans\' unique ability to create and manipulate complex abstract structures, whether in language, mathematics or music. Yet the mechanisms by which children develop such abstract thinking, and the role of education and structured experiences such as musical practice in shaping these abilities remain unclear. To explore these questions, we conducted cross-sectional behavioral experiments with 566 children aged 4 to 8, spanning four educational grades, half of whom participated in a violin training program since the age of four. Two experiments examined how children encode, process and compress auditory sequences and visual patterns, while a third examined their sensitivity to geometric regularities. Our results reveal the emergence of symbolic reasoning as early as the start of formal schooling, yet with deeper abstraction as a function of grade. By first grade, children encoded complex auditory sequences within a Language of Thought (LoT) similar to adults. Additionally, when confronted with quadrilaterals, children showed increasing sensitivity to geometric regularities, suggesting a developmental transition from perceptual to symbolic reasoning. However, we did not observe significant impact of musical practice on abstraction abilities across any of the domains tested. We discuss whether and how the impact of education and extracurricular activities such as music could be enhanced.