Western Armenian is a low-resource language spoken by the Armenian Diaspora residing in various places of the world. Although having content on the internet as well as a relatively rich literary heritage for a minority language, there is no data for the machine translation task and only a very limited amount of labeled data for other NLP tasks. In this work, we build the first machine translation system between Western Armenian and English. We explore different techniques for data collection and evaluate their impact in this very low-resource scenario. Then, we build the machine translation system while focusing on the possibilities of performing knowledge transfer from Eastern Armenian. The system is finetuned with the data collected for the first Western Armenian-English parallel corpus, which contains a total of approximately 147k sentence pairs, whose shareable part of 52k examples was made open-source. The best system through the experiments performs with a BLEU score of 29.8 while translating into English and 17 into Western Armenian.