A story’s timeline is a funny thing because you can play with it–chop it up and move pieces around–and the audience can still figure out what happened. Mysteries are particularly good about this because there are, in fact, two time lines: there’s the timeline of what happened and the timeline of the detective figuring out what happened in the first time line. Often, the detective discovers the crime first and then clues are revealed out of order. Part of the skill of a detective is in putting together a proper narrative in time order.
That means literary folks have traditional ways of dealing with timeline distortions.
Prologue. This usually presents something that happened before the story proper begins, anywhere from one hour earlier to centuries earlier. It is presented as essential information or as a dramatic hook that sets up the story. Orson Scott Card, in his book Writing Science Fiction and Fantasy, warns against prologues whose only purpose is to give back story. Instead, he prefers that a story start in present time with an immediate scene. And in general, I agree, while still reserving the idea that sometimes a dramatic prologue does work.
Second Chapter Back Story. Another common solution to timeline shifts is a second chapter that goes backward to explain the story more and weave in background. It is a solution that can work: you’ve hooked the reader with a dramatic, immediate scene in the first chapter and maybe you do have the leisure to go back and explain. The danger is that this becomes an expository chapter with no scenes, no immediate conflict. If you choose this, be sure to embed explanations in scenes, or write scenes that took place in the past. Just be sure to use scenes.
Flashbacks. These are sections where the story returns to a former moment and can be very brief or fully fleshed out. The rule of thumb is to put a flashback at the moment when it will have the most emotional impact. This means that what happened in the story past will carry forward some emotion to the present situation and change it in some way, deepen the emotion, twist the emotion, negate the emotion–something. If you present a flashback and nothing changes, then it should be omitted. Read more: Flashback Scenes: Dos and Don’ts
The solution for you story lies in the story itself. Your first draft told you the story in detail; the second and subsequent drafts should be about the most dramatic way to tell that story. For dramatic purposes, to keep the reader glued to the story, you need to discover the best way to present the narrative and that may mean time shifting some parts.
One caution: the reader should never be confused about when and where the story is taking place (unless, of course, you have a very good reason). Use time words to keep the reader oriented: First, later, ten years ago, yesterday, the next day and so on. Sometimes you need more specific clues: in the potentially confusing movie, INCEPTION, they use different weather, distinctly different settings to make sure the reader knows exactly when and where they are. Make sure you signal time shifts with as much skill!