Over the last decade, society and industries have undergone rapid digitization that is expected to lead to the evolution of the cyber-physical continuum. End-to-end deterministic communications infrastructure is the essential glue that will bridge the digital and physical worlds of the continuum. We describe the state of the art and open challenges with respect to contemporary deterministic communications and compute technologies- 3GPP 5G, IEEE Time-Sensitive Networking, IETF DetNet, OPC UA as well as edge computing. While these technologies represent significant technological advancements towards networking Cyber-Physical Systems (CPS), we argue in this paper that they rather represent a first generation of systems that are still limited in different dimensions. In contrast, realizing future deterministic communications systems requires, firstly, seamless convergence between these technologies and, secondly, scalability to support heterogeneous (time-varying requirements) arising from diverse CPS applications. In addition, future deterministic communication networks will have to provide such characteristics end-to-end, which for CPS refers to the entire communication and computation loop, from sensors to actuators. In this paper, we discuss the state of the art regarding the main challenges towards these goals: predictability, end-to-end technology integration, end-to-end security, and scalable vertical application interfacing. We then present our vision regarding viable approaches and technological enablers to overcome these four central challenges. In particular, we argue that there is currently a window of opportunity to establish, through 6G standardization, the foundations for a scalable and converged deterministic communications and compute infrastructure. Key approaches to leverage in that regard are 6G system evolutions, wireless-friendly 6G integration with TSN and DetNet, novel end-to-end security approaches, efficient edge-cloud integrations, data-driven approaches for stochastic characterization and prediction, as well as leveraging digital twins towards system awareness.