Artificial Intelligence as a Service (AIaaS) in industrial environments requires low latency, scalability, and adaptive orchestration across heterogeneous computing infrastructures. This work presents ADAPT, an architecture-agnostic platform designed to dynamically provision, migrate, and scale Artificial Intelligence (AI) services under real industrial conditions throughout the Edge–Cloud Continuum (ECC). The validation was conducted in an operational testbed composed of sensorized machining equipment, edge devices, and a cloud cluster running multi-architecture containerized services orchestrated by HashiCorp Nomad, configured with heterogeneous compute nodes, affinity rules, architecture-aware scheduling, and load-based allocation policies. The evaluation covers three computational arrangements: (i) edge-only, (ii) cloud-only, and (iii) hybrid. Performance was assessed through provisioning time, cold start time, service execution time, and resource utilization, with each test executed five times to ensure reproducibility. Results show that ADAPT effectively manages workload placement, responding to orchestration policies and operational variations while maintaining low-latency inference at the edge and scalable processing in the cloud. These findings highlight the platform’s potential to enable adaptive and robust AI services within Industry 4.0 environments.