This paper presents the Customer Experience (CX) Simulator, a novel framework designed to assess the effects of untested web-marketing campaigns through user behavior simulations. The proposed framework leverages large language models (LLMs) to represent various events in a user's behavioral history, such as viewing an item, applying a coupon, or purchasing an item, as semantic embedding vectors. We train a model to predict transitions between events from their LLM embeddings, which can even generalize to unseen events by learning from diverse training data. In web-marketing applications, we leverage this transition prediction model to simulate how users might react differently when new campaigns or products are presented to them. This allows us to eliminate the need for costly online testing and enhance the marketers' abilities to reveal insights. Our numerical evaluation and user study, utilizing BigQuery Public Datasets from the Google Merchandise Store, demonstrate the effectiveness of our framework.