This theoretical article aims to create a conceptual framework for future research on digital methods for assessing cognition in children through estimating shared intentionality, different from assessing through behavioral markers. It shows the new assessing paradigm based directly on the evaluation of parent-child interaction exchanges (protoconversation), allowing early monitoring of children's developmental trajectories. This literature analysis attempts to understand how cognition is related to emotions in interpersonal dynamics and whether assessing these dynamics shows cognitive abilities in children. The first part discusses infants' unexpected achievements, observing the literature about children's development. The analysis supposes that due to the caregiver's help under emotional arousal, newborns' intentionality could appear even before it is possible for children's intention to occur. The emotional bond evokes intentionality in neonates. Therefore, they can manifest unexpected achievements while performing them with caregivers. This outcome shows an appearance of protoconversation in adult-children dyads through shared intentionality. The article presents experimental data of other studies that extend our knowledge about human cognition by showing an increase of coordinated neuronal activities and the acquisition of new knowledge by subjects in the absence of sensory cues. This highlights the contribution of interpersonal interaction to gain cognition, discussed already by Vygotsky. The current theoretical study hypothesizes that if shared intentionality promotes cognition from the onset, this interaction modality can also facilitate cognition in older children. Therefore in the second step, the current article analyzes empirical data of recent studies that reported meaningful interaction in mother-infant dyads without sensory cues. It discusses whether an unbiased digital assessment of the interaction ability of children is possible before the age when the typical developmental trajectory implies verbal communication. The article develops knowledge for a digital assessment that can measure the extent of children's ability to acquire knowledge through protoconversation. This specific assessment can signalize the lack of communication ability in children even when the typical trajectory of peers' development does not imply verbal communication.