The increasing adoption of multi-tenant cloud infrastructures has introduced major challenges for digital forensic investigations due to distributed resources, dynamic workloads, and tenant isolation requirements. Traditional centralized forensic approaches often fail to provide timely evidence acquisition and scalable incident response in real-time environments. This study proposes an edge-cloud forensic readiness framework designed to support continuous monitoring and rapid forensic analysis in multi-tenant cloud systems. The proposed framework combines lightweight edge-based evidence collection with centralized cloud-side forensic processing. Edge agents monitor local activities and collect system events with minimal resource consumption, while cloud services perform correlation, anomaly detection, and forensic analysis using machine learning techniques. The implementation was simulated using Python-based technologies including SimPy, Flask, psutil, TinyDB, and scikit-learn. Experimental evaluation was conducted under multiple tenant-load scenarios using forensic traceability, latency, false positive rate, and isolation breach probability as performance metrics. The results demonstrate that the framework maintains high forensic traceability while reducing response latency compared with traditional cloud-only approaches. However, increasing tenant density also increases isolation risks and processing overhead, highlighting important scalability-security trade-offs in shared infrastructures. The findings indicate that integrating edge computing with forensic readiness mechanisms can significantly improve real-time digital forensic capabilities in distributed cloud environments while preserving tenant-aware monitoring and operational efficiency.