Infants are powerful learners. A large corpus of experimental paradigms demonstrate that infants readily learn distributional cues of name-object co-occurrences. But infants’ natural learning environment is cluttered: every heard word has multiple competing referents in view. Here we ask how infants start learning name-object co-occurrences in naturalistic learning environments that are cluttered and where there is much visual ambiguity. The framework presented in this paper integrates a naturalistic behavioral study and an application of a machine learning model. Our behavioral findings suggest that in order to start learning object names, infants and their parents consistently select a set of a few objects to play with during a set amount of time. What emerges is a frequency distribution of a few toys that approximates a Zipfian frequency distribution of objects for learning. We find that a machine learning model trained with a Zipf-like distribution of these object images outperformed the model trained with a uniform distribution. Overall, these findings suggest that to overcome referential ambiguity in clutter, infants may be selecting just a few toys allowing them to learn many distributional cues about a few name-object pairs.