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Infant vocal babbling strongly relies on jaw oscillations, especially at the stage of canonical babbling, which underlies the syllabic structure of world languages. In this paper, we propose, model and analyze an hypothesis to explain this predominance of the jaw in early babbling. This hypothesis states that general stochastic optimization principles, when applied to learning sensorimotor control, automatically generate ordered babbling stages with a predominant exploration of jaw movements in early stages. The reason is that those movements impact the auditory effects more than other articulators. In previous computational models, such general principles were shown to selectively freeze and free degrees of freedom in a model reproducing the proximo-distal development observed in infant arm reaching. The contribution of this paper is to show how, using the same methods, we are able to explain such patterns in vocal development. We present three experiments. The two first ones show that the recruitment order of articulators emerging from stochastic optimization depends on the target sound to be achieved but that on average the jaw is largely chosen as the first recruited articulator. The third experiment analyses in more detail how the emerging recruitment order is shaped by the dynamics of the optimization process.