Can you write a novel without knowing how the plot ends?

Yep, it’s called pantsing or discovery writing. A lot of writers do novels this way because they enjoy the journey. It usually results in a longer, looser book, but often these books are richer as a result. Certain genres demand tighter plotting, e.g. mystery, while other genres are better suited to pantsers (e.g. fantasy), although a good writer can bend conventions to their heart’s content anyway.

I’m something of a plotter, but I often get started with only a vague idea of how the novel is actually going to end. The final chapters are the ones that usually get changed the most in the rewrite, because once I actually understand who the characters are and what the story arc really is, I am much more ready to write a decent ending.