This study is a qualitative investigation of caregiver-child interactions, involving 15 autistic children who are in the early stages of language learning. Data consisted of 15-min videos of free-play interactions recorded in a University clinic. We use conversation analysis to examine the sequence organization of proposal episodes, where the caregiver proposes some course of action regarding the child's play activity. Prior work has used a speech act theoretical framework to identify follow-in directives, which are similar to proposals, but identified at the utterance level rather than at the level of social action. According to conversation analysis, social actions are implemented over multiple interactional turns and produced in collaboration between interaction partners. Our analysis showed that caregivers design their talk in ways that enable autistic children's participation in interactional turn-taking by forecasting the upcoming proposal. They also socialize children into expectations around turn-taking, by providing an "interaction envelope" around children's conduct so that it can be construed as completing interactional sequences. Finally, we show how autistic children can display an orientation to turn-taking by timing their interactive moves to occur at transitional moments in the interaction in ways similar to adult conversational turn-taking.