Although recent advancements in learning-based analog circuit design automation have tackled tasks such as topology generation, device sizing, and layout synthesis, efficient performance evaluation remains a major bottleneck. Traditional SPICE simulations are time-consuming, while existing machine learning methods often require topology-specific retraining or manual substructure segmentation for fine-tuning, hindering scalability and adaptability. In this work, we propose ZeroSim, a transformer-based performance modeling framework designed to achieve robust in-distribution generalization across trained topologies under novel parameter configurations and zero-shot generalization to unseen topologies without any fine-tuning. We apply three key enabling strategies: (1) a diverse training corpus of 3.6 million instances covering over 60 amplifier topologies, (2) unified topology embeddings leveraging global-aware tokens and hierarchical attention to robustly generalize to novel circuits, and (3) a topology-conditioned parameter mapping approach that maintains consistent structural representations independent of parameter variations. Our experimental results demonstrate that ZeroSim significantly outperforms baseline models such as multilayer perceptrons, graph neural networks and transformers, delivering accurate zero-shot predictions across different amplifier topologies. Additionally, when integrated into a reinforcement learning-based parameter optimization pipeline, ZeroSim achieves a remarkable speedup (13x) compared to conventional SPICE simulations, underscoring its practical value for a wide range of analog circuit design automation tasks.