Young children demonstrate early abilities to understand their physical world, estimating depth, motion, object coherence, interactions, and many other aspects of physical scene understanding. Children are both data-efficient and flexible cognitive systems, creating competence despite extremely limited training data, while generalizing to myriad untrained tasks -- a major challenge even for today's best AI systems. Here we introduce a novel computational hypothesis for these abilities, the Zero-shot Visual World Model (ZWM). ZWM is based on three principles: a sparse temporally-factored predictor that decouples appearance from dynamics; zero-shot estimation through approximate causal inference; and composition of inferences to build more complex abilities. We show that ZWM can be learned from the first-person experience of a single child, rapidly generating competence across multiple physical understanding benchmarks. It also broadly recapitulates behavioral signatures of child development and builds brain-like internal representations. Our work presents a blueprint for efficient and flexible learning from human-scale data, advancing both a computational account for children's early physical understanding and a path toward data-efficient AI systems.