The default paradigm for the forecasting of human behavior in social conversations is characterized by top-down approaches. These involve identifying predictive relationships between low level nonverbal cues and future semantic events of interest (e.g. turn changes, group leaving). A common hurdle however, is the limited availability of labeled data for supervised learning. In this work, we take the first step in the direction of a bottom-up self-supervised approach in the domain. We formulate the task of Social Cue Forecasting to leverage the larger amount of unlabeled low-level behavior cues, and characterize the modeling challenges involved. To address these, we take a meta-learning approach and propose the Social Process (SP) models--socially aware sequence-to-sequence (Seq2Seq) models within the Neural Process (NP) family. SP models learn extractable representations of non-semantic future cues for each participant, while capturing global uncertainty by jointly reasoning about the future for all members of the group. Evaluation on synthesized and real-world behavior data shows that our SP models achieve higher log-likelihood than the NP baselines, and also highlights important considerations for applying such techniques within the domain of social human interactions.