Writer's Fallout Shelter

Before I ask my question, here are some happy colors to celebrate Liam's return from the anesthetized.


Now, I would like to know what anyone on the forum thinks of this:
         I have a book that just refuses to be divided into chapters. It has scene breaks, but these lie between the activities of different characters who don't interact until they all get mixed up in the same conflict. Putting dates at the beginning of the "sections" is more natural, because all of the main action in this story takes place within the space of about a week.
         So many publishers ask for "the first three chapters." Must I engineer a way for there to be chapters?