Emerging applications, such as large-scale engineering computing, are accelerating the development of wide-area deterministic networks to accommodate increasing traffic demands and differentiated service requirements. However, existing technologies face substantial scalability and coordination challenges in multi-domain, heterogeneous environments, rendering them unsuitable for large-scale deployments. Moreover, relying on a single technological paradigm is insufficient to support an open, wide-area deterministic network at scale. To overcome these limitations, this paper proposes a large-scale deterministic network architecture based on open services availability first (OSAF). The proposed architecture employs cross-domain collaboration and hierarchical management mechanism, to support tiered resource scheduling and dynamic path optimization in heterogeneous cross-domain networks. In addition, a Transformer-based reinforcement learning algorithm (T-DRL) is introduced, enabling OSAF to optimize routing and scheduling decisions with a latency-first objective, thereby enhancing deterministic quality of service (QoS) guarantees for end-to-end differentiated open services.