What I mean is, does my story have to start with my main character being introduced, or can I start with their parents and then ease into the main character after a time skip?
I've seen this done frequently, in well-known books, so it clearly CAN be done. With that said, I've rarely personally found it to be a good idea. The risk is that the reader gets invested in the secondary characters, and resists the move to the main ones. There's two books, by very good authors I like a lot (Enchantress of Florence, Rushdie, and Stars in My Pocket..., Delany), that I ended up disliking, just because the characters in the prologue were so much more interesting to me than the actual main characters. Conversely, if the secondary characters aren't interesting or compelling, you risk losing your reader right at the start of the book, and maybe for nothing.
The places I've seen it work best are where the prologue is short, action-oriented, and sets the context for the main story. An example is the start of the first Harry Potter. It gives us the context that this is a magical world, that there's a battle of good-and-evil, and that the main character is someone special, even if he doesn't appear to be. Arguably you don't NEED any of that to begin the book, but it does give an intriguing contrast to the seemingly mundane scene that introduces the eleven-year-old Harry directly.
Starting with the parents, or sometimes even the distant ancestors of the main character, is not necessarily my cup of tea, but it's not uncommon. Les Miserables, The Tin Drum, White Teeth and The Moor's Last Sigh all do this, to name just a few. I'd say it's suited best, however, to a sprawling epic. If your novel isn't thousands of pages long, I'd save the parents' history for your backstory. You should always know more about the characters, and where they come from, than you actually put on the page. If you save it, you have it when you need it.
Rather than asking people if you "have" to do something, I would suggest asking yourself "why" you want to do something. As an author you can do nearly anything you want. Some things will work, some things won't, but there aren't really any hard and fast rules. Chris in his answer gave some good examples of books that broke normal conventions, and did so successfully.
In your case, I would ask myself the following questions and see where the answers lead me as an author:
- Why do I want to start with a secondary character?
- What will be gained by starting out with the family?/What will be lost if I start with the main character?
- How much narrative time (how many pages/chapters) will take place between the initial setup and the time skip?
- What do I want readers to get out of the opening? What emotional investments do I want them to form?
- Are the pre-timeskip events interesting enough to draw the reader in and get them invested in the story as a whole?
- Is the "lost time" (the time between the introduction and the end of the time skip) relevant to the story? Is it important/interesting?
Depending on your answers to these questions (and more), you can ultimately determine "In this particular story, is there value in avoiding starting with the main character?"
Be aware of the consequences
As with all things in writing, you can do it, but doing so will impact how your writing comes across to readers. There are both drawbacks and advantages to using this technique and you should be aware of both when deciding if you should use it.
The main drawbacks are the potential of disconnection with your eventual main character. Your audience thought they were getting one thing, began getting attached to the first character you present only for you to bait-and-switch. I know of several readers who have simply put down books at this point because they no longer felt connected to the story. Notably I think of the dystopian novel Wool by Hugh Howey, I personally enjoy it but several other people I have recommended it to struggled to get past this point.
The advantages of using this technique depend on your execution. Done properly it can introduce the settings and stakes of your story in a way that you could never do with only a single main character. It can help start your narrative in a moment of action without requiring your main character to have experience it. It provides a window of exposition beyond what you may normally see, letting you set up your world in more detail, giving more weight to what makes your main character special.
To again draw from the Wool example. In the first section of the novel we see how things normally play out for people in this world. What the consequences and stakes for their actions are, and the likely outcome. So when we meet the main character we can appreciate how they breaks these norms. Without the setup chapters/characters we, as readers, wouldn't comprehend the gravity of the decisions the main character makes or appreciate what makes them special.
What are your trying to achieve?
When using a major narrative technique like this the key thing to keep in mind is what are your trying to achieve with this section? What point are your trying to portray to the reader? Keep that in mind and try to objectively assess if your work is achieving that goal. Don't hold on to a technique that isn't having the impact you want purely for the sake of using it.
Ultimately the answer is, you can do it if you think it works. Try it, write a draft of your story and then step back and see if it is working the way you intend. If the drawbacks outweigh the benefits, consider reworking it. If not, congratulations you successfully wrote a thing!
That depends how you define 'main character'. Usually a main character in a story is the one the narrator would be most familiar with and interested in / know the most about - therefore that should be the focus from the start of the story. If that involves describing the main characters' surroundings, background, upbringing etc before actually introducing them then so be it, but I'd advise you not to let the start be completely irrelevant to the main characters, otherwise you risk losing readers' interest as the narrative shifts focus.
It depends on the amount of point-of-view characters you are using.
Is your book using the point of view of a single main character?
If your story follows only a single character, you might want to avoid it, though it's still possible and fairly common, though occasionally poorly executed. A prologue can be completely separate from the main story, as long as the reader knows that it's a prologue and the transfer to the new point of view is clear even to a not that attentive reader. Don't make the prologue too long, or the expectations of the readers will be misled.
Does your book have a large cast of point-of-view characters it switches between?
Then it's absolutely no problem not to start with the "main" character. You can start with any character, even a throwaway who will never appear again. In books featuring large casts of characters, e.g. Game of Thrones (which I haven't actually read), characters change constantly anyways. Some die or disappear, new ones join the story, so having a few characters more doesn't make a difference.
In order to demonstrate that it is not necessary, we can see that some very successful pieces of screen-writing did not introduce all of their main characters straight away.
Although Frances McDormand's character is the film's central role, she does not appear on the screen until over 33 minutes (or 1/3) into the film.
Leonardo DiCaprio does not appear until one hour and three minutes in.
These are just two examples of many that demonstrate there is no hard-and-fast rule that you must introduce all of your main characters immediately.
Where the author deliberately tricks the audience into mistaking who the protagonist is, it is called a False protagonist:
In fiction, a false protagonist is a literary technique, often used to make the plot more jarring or more memorable by defying the audience's preconceptions, whereby a character who the audience assumes is the protagonist is later revealed not to be.
A false protagonist is presented at the start of the fictional work as the main character, but is then removed from the role, often killed (usually for shock value or as a plot twist) or relegated to a different role in the story (i.e. making them a lesser character, a character who leaves the story, or revealing the character to actually be the antagonist).
What genre are you writing in? What's appropriate in one will probably not be appropriate for another.
E.g. Fantasy novels often start with a hefty prologue that tells the reader something about the world the story takes place in, but does not feature the protagonist, because their introduction needs to be drawn out. Game of Thrones is a great example, it introduces the central concepts of the Night Watch, Wall, North, Others, etc. A YA high-school focused novel doesn't need any foundation building and shouldn't waste any time until introducing the protagonist(s).
Also, are you trying to write something that you expect to try and sell commercially? Because if you are, you need something that will hook a reader, whether it's browsing in a book store, or reading the preview in Kindle. If you have a scene in your mind that's compact and captivating, but should logically take place in the middle of the book, pulling a bait and switch and putting it first is acceptable for commercial reasons, even though it might slightly degrade the flow of the story.
You can structure your book in ways where you can make this work.
Hospital Station is the first book in the Sector General series by James White. The book is divided into short stories that take place in a hospital out in space, centered around junior surgeon Dr. Conway, that reports to the head of the psychology department, one Major O'Mara. However, the very first story is actually about O'Mara's humble beginnings as a construction worker, establishing him as a brilliant psychologist.
In the "main" stories, O'Mara is rather secondary, but his relationship to Conway is important. This character's input is given weight for the readers by means of that "prologue" story, so to speak.
As another example, the characters that appear in the prologues for the various Game of Thrones books have a relationship to the main characters that is tenuous at best.
So, yes, it can be done, but as other answers have indicated, you do risk alienating your readers. I would say it comes down to managing their expectations, and the right narrative structure can certainly help with that.
Adding in another fictional element and example, we see this technique used in The Last of Us (video game) where you start the game as the main protagonists daughter.
The intro to that game creates a very strong purpose and drive for the main character. Here you are setting up the main story through
the tragedy of a character that we only meet in the first chapter where she dies in the arms of her father (the protagonist).
There's a rather interesting Elders play video of older people playing the intro sequence and their reactions to the storytelling of it.
Setting an intro up like this, while not having the protagonist as the main character, ultimately makes the player/reader have a stronger bond with him. So it can be used very well in storytelling when used correctly.