Well, 'the commencement' is another way to refer to the start of a story. It's like the story is about to commence, start its journey, and draw the reader in from that very first moment.
The start of a story can also be called the 'opening'. For example, in many novels, the opening sets the scene, introduces the main characters or gives a hint about the main conflict.
A yarn can also be another name for a story. This term is often used in a more informal or folksy way. People might say 'spin a yarn' which means to tell a story, usually one that is interesting or perhaps a little exaggerated.
A mystery story can also be called a whodunit. This term emphasizes the central question in many mystery stories, which is 'who done it' - who committed the crime or caused the mystery in the first place. It's a very common and fun way to refer to this genre, especially when you're focused on the mystery of the perpetrator's identity.