Routine childhood growth surveillance is a cornerstone of pediatric care. Growth pattern abnormalities are often early manifestations of chronic disease. Yet subtle abnormalities are frequently underrecognized, leading to diagnostic delays and avoidable morbidity. We introduce SPROUT (System for Pediatric Recognition Of Undiagnosed Trajectories), a generalized, multi-agent large language model (LLM) reasoning system designed to identify a broad spectrum of pediatric growth-related conditions from longitudinal electronic health records (EHRs) earlier than standard clinical practice. Using a large pediatric primary care EHR dataset, we developed and validated SPROUT as a two-stage system. First, a highly specific LLM screener flags concerning longitudinal growth patterns. Second, an Orchestrator module coordinates a multidisciplinary panel of LLM agents to generate a ranked differential diagnosis. To correct systemic reasoning errors, a Trainer module injects meta-knowledge into the panel via a dedicated "Learner" agent. Diagnostic capability was evaluated using a walk-forward, visit-by-visit simulation leading up to the diagnosis date. The SPROUT screener model achieved 98% (83/85) specificity and 28% (9/32) sensitivity on a gold-standard dataset of pediatric primary care patients when evaluated one year before the index date, and 100% specificity and 47% sensitivity when evaluated using longitudinal data up to the day of diagnosis. When applied to 300 control patients (i.e., healthy or undiagnosed), the screener flagged 15. Subsequent expert panel review confirmed high suspicion for undiagnosed pathology in 33% (5/15) of these cases. In chronological walk-forward validation on disease cases, the diagnostic engine identified conditions well before standard-of-care documentation. One year prior to clinical diagnosis, the system achieved sensitivities of 81% for type 1 diabetes mellitus, 56% for pituitary disorders, and 44% for celiac disease. The SPROUT multi-agent system demonstrates the ability to detect a significant portion of latent growth-related pediatric conditions months to years before current clinical standards while minimizing false positives. These results support its potential as a decision support tool for reducing diagnostic delays in pediatric care.