Henry Ford's Model T is often cited as a major step towards complete interchangeability, though even it wasn't perfect. Ford's assembly line and mass production techniques significantly increased the degree of interchangeability, making repairs and manufacturing far more efficient. However, achieving *complete* interchangeability, where any part from any Model T could be swapped with any other, was an ideal more than a reality. Variations and tolerances existed.
Therefore, there's no definitive answer to your question. The development of interchangeable parts was a process, not a single event associated with a specific car.