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, our findings reveal stark disparities in translation performance across test sets, with BLEU scores reaching as high as 21.2 on materials from the language manual, in contrast to a maximum of 4.4 on a test set provided by a native speaker. These results underscore the importance of diverse and representative corpora in assessing MT for low-resource languages. Our research provides insights into few-shot LLM prompting for low-resource MT, and makes available an initial corpus for the Mambai language.