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Natural language processing (NLP) algorithms are rapidly improving but often struggle when applied to out-of-distribution examples. A prominent approach to mitigate the domain gap is domain adaptation, where a model trained on a source domain is adapted to a new target domain. We present a new learning setup, ``domain adaptation from scratch'', which we believe to be crucial for extending the reach of NLP to sensitive domains in a privacy-preserving manner. In this setup, we aim to efficiently annotate data from a set of source domains such that the trained model performs well on a sensitive target domain from which data is unavailable for annotation. Our study compares several approaches for this challenging setup, ranging from data selection and domain adaptation algorithms to active learning paradigms, on two NLP tasks: sentiment analysis and Named Entity Recognition. Our results suggest that using the abovementioned approaches eases the domain gap, and combining them further improves the results.