Studying early speech development at scale requires automatic tools, yet automatic phoneme recognition, especially for young children, remains largely unsolved. Building on decades of data collection, we curate TinyVox, a corpus of more than half a million phonetically transcribed child vocalizations in English, French, Portuguese, German, and Spanish. We use TinyVox to train BabAR, a cross-linguistic phoneme recognition system for child speech. We find that pretraining the system on multilingual child-centered daylong recordings substantially outperforms alternatives, and that providing 20 seconds of surrounding audio context during fine-tuning further improves performance. Error analyses show that substitutions predominantly fall within the same broad phonetic categories, suggesting suitability for coarse-grained developmental analyses. We validate BabAR by showing that its automatic measures of speech maturity align with developmental estimates from the literature.