Recent evidence reveals a precocious link between language and cognition in human infants: listening to their native language supports infants' core cognitive processes, including object categorization, and does so in a way that other acoustic signals (e.g., time-reversed speech; sine-wave tone sequences) do not. Moreover, language is not the only signal that confers this cognitive advantage: listening to vocalizations of non-human primates also supports object categorization in 3- and 4-month-olds. Here, we move beyond primate vocalizations to clarify the breadth of acoustic signals that promote infant cognition. We ask whether listening to birdsong, another naturally produced animal vocalization, also supports object categorization in 3- and 4-month-old infants. We report that listening to zebra finch song failed to confer a cognitive advantage. This outcome brings us closer to identifying a boundary condition on the range of non-linguistic acoustic signals that initially support infant cognition.