In this work, we investigate the Meta PL unsupervised domain adaptation framework for Automatic Speech Recognition (ASR). We introduce a Multi-Stage Domain Adaptation pipeline (MSDA), a sample-efficient, two-stage adaptation approach that integrates self-supervised learning with semi-supervised techniques. MSDA is designed to enhance the robustness and generalization of ASR models, making them more adaptable to diverse conditions. It is particularly effective for low-resource languages like Greek and in weakly supervised scenarios where labeled data is scarce or noisy. Through extensive experiments, we demonstrate that Meta PL can be applied effectively to ASR tasks, achieving state-of-the-art results, significantly outperforming state-of-the-art methods, and providing more robust solutions for unsupervised domain adaptation in ASR. Our ablations highlight the necessity of utilizing a cascading approach when combining self-supervision with self-training.