As large language models (LLMs) become more integrated into daily life, it is crucial to foster AI literacy among high school stu- dents. However, most AI courses target college-level learners and assume prior knowledge, while high schools often lack the foundational curricu- lum and infrastructure for traditional LLM education. To bridge this gap, we present a hackathon-based framework that makes LLM learning acces- sible, engaging, and hands-on. The program combines interactive lectures on core LLM concepts with a guided competition where students fine- tune models and build real-world applications, such as healthcare chat- bots. This approach boosts motivation, programming skills, and practical understanding. Post-hackathon survey results show students gained both functional LLM experience and foundational knowledge. Furthermore, our framework can be extended to broader audiences, including learners without prior AI/NLP experience, offering a rapid, application-driven introduction to LLMs.