General continual learning (GCL) is a broad concept to describe real-world continual learning (CL) problems, which are often characterized by online data streams without distinct transitions between tasks, i.e., blurry task boundaries. Such requirements result in poor initial performance, limited generalizability, and severe catastrophic forgetting, heavily impacting the effectiveness of mainstream GCL models trained from scratch. While the use of a frozen pretrained backbone with appropriate prompt tuning can partially address these challenges, such prompt-based methods remain suboptimal for CL of remaining tunable parameters on the fly. In this regard, we propose an innovative approach named MISA (Mask and Initial Session Adaption) to advance prompt-based methods in GCL. It includes a forgetting-aware initial session adaption that employs pretraining data to initialize prompt parameters and improve generalizability, as well as a non-parametric logit mask of the output layers to mitigate catastrophic forgetting. Empirical results demonstrate substantial performance gains of our approach compared to recent competitors, especially without a replay buffer (e.g., up to 18.39, 22.06, and 11.96% points performance lead on CIFAR-100, Tiny-ImageNet, and ImageNet-R, respectively). Moreover, our approach features the plug-in nature for prompt-based methods, independence of replay, ease of implementation, and avoidance of CL-relevant hyperparameters, serving as a strong baseline for GCL research. Our source code is publicly available at https://github.com/kangzhiq/MISA