Infants have a sophisticated behavioral and cognitive repertoire suggestive of a capacity for conscious reflection. Yet, demonstrating conscious access in infants remains challenging, mainly because they cannot report their thoughts. Here, to circumvent this problem, we studied whether an electrophysiological signature of consciousness found in adults, corresponding to a late nonlinear cortical response [~300 milliseconds (ms)] to brief pictures, already exists in infants. We recorded event-related potentials while 5-, 12-, and 15-month-old infants (N = 80) viewed masked faces at various levels of visibility. In all age groups, we found a late slow wave showing a nonlinear profile at the expected perceptual thresholds. However, this late component shifted from a weak and delayed response in 5-month-olds (starting around 900 ms) to a more sustained and faster response in older infants (around 750 ms). These results reveal that the brain mechanisms underlying the threshold for conscious perception are already present in infancy but undergo a slow acceleration during development.