This study pioneers the use of synthetically generated data for training generative models in document-level text simplification of German texts. We demonstrate the effectiveness of our approach with real-world online texts. Addressing the challenge of data scarcity in language simplification, we crawled professionally simplified German texts and synthesized a corpus using GPT-4. We finetune Large Language Models with up to 13 billion parameters on this data and evaluate their performance. This paper employs various methodologies for evaluation and demonstrates the limitations of currently used rule-based metrics. Both automatic and manual evaluations reveal that our models can significantly simplify real-world online texts, indicating the potential of synthetic data in improving text simplification.