Deep Active Learning (AL) techniques can be effective in reducing annotation costs for training deep models. However, their effectiveness in low- and high-budget scenarios seems to require different strategies, and achieving optimal results across varying budget scenarios remains a challenge. In this study, we introduce Dynamic Coverage & Margin mix (DCoM), a novel active learning approach designed to bridge this gap. Unlike existing strategies, DCoM dynamically adjusts its strategy, considering the competence of the current model. Through theoretical analysis and empirical evaluations on diverse datasets, including challenging computer vision tasks, we demonstrate DCoM's ability to overcome the cold start problem and consistently improve results across different budgetary constraints. Thus DCoM achieves state-of-the-art performance in both low- and high-budget regimes.