This work demonstrates that substantial gains in zero-shot dialogue state tracking (DST) accuracy can be achieved by increasing the diversity of training data using synthetic data generation techniques. Current DST training resources are severely limited in the number of application domains and slot types they cover due to the high costs of data collection, resulting in limited adaptability to new domains. The presented work overcomes this challenge using a novel, fully automatic data generation approach to create synthetic zero-shot DST training resources. Unlike previous approaches for generating DST data, the presented approach generates entirely new application domains to generate dialogues, complete with silver dialogue state annotations and slot descriptions. This approach is used to create the D0T dataset for training zero-shot DST models, which covers an unprecedented 1,000+ domains. Experiments performed on the MultiWOZ benchmark indicate that training models on diverse synthetic data yields a performance improvement of +6.7% Joint Goal Accuracy, achieving results competitive with much larger models.