Cross-Domain Few-Shot Segmentation aims to segment categories in data-scarce domains conditioned on a few exemplars. Typical methods first establish few-shot capability in a large-scale source domain and then adapt it to target domains. However, due to the limited quantity and diversity of target samples, existing methods still exhibit constrained performance. Moreover, the source-trained model's initially weak few-shot capability in target domains, coupled with substantial domain gaps, severely hinders the effective utilization of target samples and further impedes adaptation. To this end, we propose Multi-view Progressive Adaptation, which progressively adapts few-shot capability to target domains from both data and strategy perspectives. (i) From the data perspective, we introduce Hybrid Progressive Augmentation, which progressively generates more diverse and complex views through cumulative strong augmentations, thereby creating increasingly challenging learning scenarios. (ii) From the strategy perspective, we design Dual-chain Multi-view Prediction, which fully leverages these progressively complex views through sequential and parallel learning paths under extensive supervision. By jointly enforcing prediction consistency across diverse and complex views, MPA achieves both robust and accurate adaptation to target domains. Extensive experiments demonstrate that MPA effectively adapts few-shot capability to target domains, outperforming state-of-the-art methods by a large margin (+7.0%).