Language model approaches have recently been integrated into binary analysis tasks, such as function similarity detection and function signature recovery. These models typically employ a two-stage training process: pre-training via Masked Language Modeling (MLM) on machine code and fine-tuning for specific tasks. While MLM helps to understand binary code structures, it ignores essential code characteristics, including control and data flow, which negatively affect model generalization. Recent work leverages domain-specific features (e.g., control flow graphs and dynamic execution traces) in transformer-based approaches to improve binary code semantic understanding. However, this approach involves complex feature engineering, a cumbersome and time-consuming process that can introduce predictive uncertainty when dealing with stripped or obfuscated code, leading to a performance drop. In this paper, we introduce ProTST, a novel transformer-based methodology for binary code embedding. ProTST employs a hierarchical training process based on a unique tree-like structure, where knowledge progressively flows from fundamental tasks at the root to more specialized tasks at the leaves. This progressive teacher-student paradigm allows the model to build upon previously learned knowledge, resulting in high-quality embeddings that can be effectively leveraged for diverse downstream binary analysis tasks. The effectiveness of ProTST is evaluated in seven binary analysis tasks, and the results show that ProTST yields an average validation score (F1 and MRR) improvement of 14.8% compared to traditional two-stage training and an average validation score of 13.4% compared to multimodal two-stage frameworks.