While it's true that J.K. Rowling had a flash of inspiration for Harry Potter at a cafe, she didn't write the first chapter on a napkin. Instead, she wrote down the initial idea, which was the concept of Harry Potter himself, along with the basic plot points of his journey, on a train journey.
She later expanded upon these notes and started writing the actual manuscript, which took her several years to complete. So, while the cafe is often credited with being the birthplace of Harry Potter, it was the train journey where the initial spark ignited.