Applications of biomolecular systems span gene writing, drug discovery, and environmental remediation. Despite their potential, biodesign remains slow and labor-intensive, often relying on trial and error. Recent advances in high-throughput sequencing, automated synthesis, and generative AI offer new opportunities but remain fragmented. We propose SYNEVO: an AI-driven, closed-loop system integrating automated protein design, and real-time experimental feedback to iteratively optimize biomolecular function. SYNEVO does not use template-based DNA replication, enabling a constraint-free generation of new genotypes, which departs from conventional evolution. We aim to validate our platform studying Zinc Finger proteins, a versatile class of DNA-binding proteins with significant therapeutic potential. Preliminary results showed that, by iteratively generating large libraries with autoregressive protein language models and experimentally testing their phenotypes, we optimized sequence selection. The measured features were fed back into the model via reinforcement learning to maximize protein enrichment scores, achieving a progressive improvement of generated phenotypes. Potentially, by continuously refining its designs with minimal human intervention, this approach will accelerate protein engineering and provide a scalable solution for engineering new biomolecules with broad use across biotechnology and synthetic biology.