Cross-lingual transfer learning without labeled target language data or parallel text has been surprisingly effective in zero-shot cross-lingual classification, question answering, unsupervised machine translation, etc. However, some recent publications have claimed that domain mismatch prevents cross-lingual transfer, and their results show that unsupervised bilingual lexicon induction (UBLI) and unsupervised neural machine translation (UNMT) do not work well when the underlying monolingual corpora come from different domains (e.g., French text from Wikipedia but English text from UN proceedings). In this work, we show how a simple initialization regimen can overcome much of the effect of domain mismatch in cross-lingual transfer. We pre-train word and contextual embeddings on the concatenated domain-mismatched corpora, and use these as initializations for three tasks: MUSE UBLI, UN Parallel UNMT, and the SemEval 2017 cross-lingual word similarity task. In all cases, our results challenge the conclusions of prior work by showing that proper initialization can recover a large portion of the losses incurred by domain mismatch.