Can we simulate a sandbox society with generative agents to model human behavior, thereby reducing the over-reliance on real human trials for assessing public policies? In this work, we investigate the feasibility of simulating health-related decision-making, using vaccine hesitancy, defined as the delay in acceptance or refusal of vaccines despite the availability of vaccination services (MacDonald, 2015), as a case study. To this end, we introduce the VacSim framework with 100 generative agents powered by Large Language Models (LLMs). VacSim simulates vaccine policy outcomes with the following steps: 1) instantiate a population of agents with demographics based on census data; 2) connect the agents via a social network and model vaccine attitudes as a function of social dynamics and disease-related information; 3) design and evaluate various public health interventions aimed at mitigating vaccine hesitancy. To align with real-world results, we also introduce simulation warmup and attitude modulation to adjust agents' attitudes. We propose a series of evaluations to assess the reliability of various LLM simulations. Experiments indicate that models like Llama and Qwen can simulate aspects of human behavior but also highlight real-world alignment challenges, such as inconsistent responses with demographic profiles. This early exploration of LLM-driven simulations is not meant to serve as definitive policy guidance; instead, it serves as a call for action to examine social simulation for policy development.