Domain adaptive semantic segmentation methods commonly utilize stage-wise training, consisting of a warm-up and a self-training stage. However, this popular approach still faces several challenges in each stage: for warm-up, the widely adopted adversarial training often results in limited performance gain, due to blind feature alignment; for self-training, finding proper categorical thresholds is very tricky. To alleviate these issues, we first propose to replace the adversarial training in the warm-up stage by a novel symmetric knowledge distillation module that only accesses the source domain data and makes the model domain generalizable. Surprisingly, this domain generalizable warm-up model brings substantial performance improvement, which can be further amplified via our proposed cross-domain mixture data augmentation technique. Then, for the self-training stage, we propose a threshold-free dynamic pseudo-label selection mechanism to ease the aforementioned threshold problem and make the model better adapted to the target domain. Extensive experiments demonstrate that our framework achieves remarkable and consistent improvements compared to the prior arts on popular benchmarks. Codes and models are available at https://github.com/fy-vision/DiGA