This study explores the use of large language models (LLMs) for translating English into Mambai, a low-resource Austronesian language spoken in Timor-Leste, with approximately 200,000 native speakers. Leveraging a novel corpus derived from a Mambai language manual and additional sentences translated by a native speaker, we examine the efficacy of few-shot LLM prompting for machine translation (MT) in this low-resource context. Our methodology involves the strategic selection of parallel sentences and dictionary entries for prompting, aiming to enhance translation accuracy, using open-source and proprietary LLMs (LlaMa 2 70b, Mixtral 8x7B, GPT-4). We find that including dictionary entries in prompts and a mix of sentences retrieved through TF-IDF and semantic embeddings significantly improves translation quality. However, translation accuracy varies between test sets, highlighting the importance of diverse corpora for evaluating low-resource MT. This research provides insights into few-shot LLM prompting for low-resource MT, and makes available an initial corpus for the Mambai language.