Adaptively responding to salient stimuli in the environment is a fundamental feature of cognitive development in early life, which is enabled by the developing brain. Understanding individual variability in how the brain supports this fundamental process is essential for uncovering neurodevelopmental trajectories and potential neurodevelopmental risks. In the present study, we used a precision functional imaging approach to probe activation in response to salient auditory stimuli and its relation to brain functional networks in individual infants. A minimum of 60 min of fMRI BOLD data with an auditory oddball paradigm were collected in ten infants with a mean postmenstrual age of 48 weeks. Results demonstrate the feasibility of conducting a precision functional imaging study to investigate individual specific responses to salient stimuli in infants. While responses to the auditory oddball were consistent across individuals in auditory processing areas, responses across the rest of the brain differed across individuals in their magnitude and time to peak. Individual specific response patterns appeared to be relatively stable and differed from other participant’s response patterns, despite fluctuations across runs. Commonalities and differences between individuals demonstrated in this sample contribute to our understanding of how the developing brain instantiates processing of salient stimuli. In this context, individual specific response patterns could be a promising target for biomarkers of normative brain and cognitive development.