Rare diseases affect over 300 million people worldwide, yet patients often endure years-long diagnostic delays that limit timely intervention and trial opportunities. Computational rare disease recognition (RDR) remains constrained by knowledge resources that are often incomplete, heterogeneous, and dependent on extensive multi-disciplinary expert curation that cannot scale. Large language models (LLMs) applied directly for end-to-end diagnosis or disease discrimination face similar knowledge bottlenecks while also raising concerns around cost, reproducibility, and data governance. Here, we introduce GEN-KnowRD, a knowledge-layer-first framework that leverages LLMs to generate schema-guided rare disease profiles, systematically assesses their quality, and constructs a computable knowledge base (PheMAP-RD) for local deployment. GEN-KnowRD integrates this knowledge into lightweight inference pipelines for both general-purpose disease screening and specialized early discrimination from longitudinal electronic health records. In tests using six public benchmarks for general-purpose screening (9,290 patients spanning 798 rare diseases), GEN-KnowRD substantially improved disease ranking versus 1) a state-of-the-art, HPO-centered diagnostic framework (up to 345.8% improvement in top-1 success), 2) advanced end-to-end LLM reasoning (up to 129.1% improvement), and 3) a variant of GEN-KnowRD instantiated with expert-curated knowledge rather than LLM-generated profiles. In two real-world cohorts for early diagnosis of idiopathic pulmonary fibrosis (511 patients) as a use case, GEN-KnowRD also demonstrated robust discrimination performance gains, supporting effective RDR during the pre-diagnostic window. These findings demonstrate that repositioning LLMs from diagnostic reasoning to the knowledge layer-decoupling knowledge construction from patient-level inference-yields stronger RDR, while providing scalable, continuously updatable, and reusable infrastructure for diagnosis, screening, and clinical research across the rare disease landscape.