In this paper we explore early musical behaviors through the lenses of the recently emerged “4E” approach to mind, which sees cognitive processes as Embodied, Embedded, Enacted, and Extended. In doing so, we draw from a range of interdisciplinary research, engaging in critical and constructive discussions with both new findings and existing positions. In particular, we refer to observational research by French pedagogue and psychologist François Delalande, who examined infants' first “sound discoveries” and individuated three different musical “conducts” inspired by the “phases of the game” originally postulated by Piaget. Elaborating on such ideas we introduce the notion of “teleomusicality,” which describes the goal-directed behaviors infants adopt to explore and play with sounds. This is distinguished from the developmentally earlier “protomusicality,” which is based on music-like utterances, movements, and emotionally relevant interactions (e.g., with primary caregivers) that do not entail a primary focus on sound itself. The development from protomusicality to teleomusicality is discussed in terms of an “attentive shift” that occurs between 6 and 10 months of age. This forms the basis of a conceptual framework for early musical development that emphasizes the emergence of exploratory, goal-directed (i.e., sound-oriented), and self-organized musical actions in infancy. In line with this, we provide a preliminary taxonomy of teleomusical processes discussing “Original Teleomusical Acts” (OTAs) and “Constituted Teleomusical Acts” (CTAs). We argue that while OTAs can be easily witnessed in infants' exploratory behaviors, CTAs involve the mastery of more specific and complex goal-directed chains of actions central to musical activity.