The computing continuum is an emerging paradigm where data is processed from the edge to the cloud, passing through the fog. Organizations distribute multiple applications in this paradigm to process large workloads and produce helpful information. Nevertheless, building and managing these systems are complex tasks requiring the orchestration of heterogeneous data through different computational sites. This paper presents a method to enable organizations to build computing continuum systems using serverless abstractions, allowing applications to be deployed through different infrastructures and their interconnection using generic data channels. This is performed through an architecture divided into four layers: processing, endpoints, data, and control. We conducted a case study based on medical data management to evaluate this method. The experimental evaluation shows the scalability of our method when increasing both the number of workers and workload.