We delineate the sequence that typically developing infants pass tasks that assess different early social cognitive skills considered precursors to theory-of-mind abilities. We compared this normative sequence to performance on these tasks in a group of autistic (AUT) children. 86 infants were administered seven tasks assessing intention reading and shared intentionality (Study 1). Infants responses followed a consistent developmental sequence, forming a four-stage scale. These tasks were administered to 21 AUT children (Study 2), who passed tasks in the same sequence. However, performance on tasks that required following others’ eye gaze and cooperating with others was delayed. Findings indicate that earlier-developing skills provide a foundation for later-developing skills, and difficulties in acquiring some early social cognitive skills in AUT children. Electronic supplementary material The online version of this article (10.1007/s10803-020-04449-9) contains supplementary material, which is available to authorized users.