A wealth of studies have investigated numerical abilities in infants and in children aged 3 or above, but research on pre-counting toddlers is sparse. Here we devised a novel version of an imitation task that was previously used to assess spontaneous focusing on numerosity (i.e. the predisposition to grasp numerical properties of the environment) to assess whether pre-counters would spontaneously deploy sequential (item-by-item) enumeration and whether this ability would rely on the object tracking system (OTS) or on the approximate number system (ANS). Two-and-a-half-year-olds watched the experimenter performing one-by-one insertion of "food tokens" into an opaque animal puppet and then were asked to imitate the puppet-feeding behavior. The number of tokens varied between 1 and 6 and each numerosity was presented many times to obtain a distribution of responses during imitation. Many children demonstrated attention to the numerosity of the food tokens despite the lack of any explicit cueing to the number dimension. Most notably, the response distributions centered on the target numerosities and showed the classic variability signature that is attributed to the ANS. These results are consistent with previous studies on sequential enumeration in non-human primates and suggest that pre-counting children are capable of sequentially updating the numerosity of non-visible sets through additive operations and hold it in memory for reproducing the observed behavior.