The increasing reliance on cloud storage across sectors has made the protection of sensitive data a critical concern especially as advances in quantum computing threaten to break traditional public-key cryptographic systems. This growing vulnerability raises urgent questions about how to secure digital assets in a post-quantum future. To address this challenge, this study aims to design, implement, and evaluate a hybrid encryption framework that combines symmetric encryption for data confidentiality with quantum-resistant public-key algorithms for key management and digital signatures. The objective was to develop a secure and practical solution that can be readily adopted using open-source tools. The system was built in a Linux-based virtual environment using an S3-compatible object storage platform, integrated with quantum-safe cryptographic libraries, and automated through scripting. Performance testing was conducted using files ranging from 100 MB to 1 GB, with metrics such as encryption and decryption time, CPU usage, upload/download latency, and internet throughput analyzed. The results showed that while quantum-safe operations added some overhead, even large files could be securely processed in under two minutes with stable system performance and no data corruption. These findings confirm that hybrid encryption models can be deployed today without specialized hardware, offering a forward-compatible and robust approach to cloud security. This work contributes a tested and reproducible framework for early adoption of quantum-safe cryptography in real-world cloud environments.