They say "the longest journey begins with a single step." Unfortunately, when that first step is the opening of your story, it often appears to be a leap across a huge chasm.
As I've said before, I think children's writers can learn a lot from flash fiction techniques because flash fiction stories have to do so much in so few words. And since finding a starting place is a problem for all kinds of writers, I found this article with 5 ways to start flash fiction stories. I'm going to focus on just two of them.
Remember that the opening of your story is called a hook. It's called that because it serves the same purpose as a fish hook -- it lets you pull the reader into your story, just as you pull a fish into your boat.
Starting with a question is a great way to start a mystery story, of course. But you don't have to use an actual question to start the story -- you can hint at one. If your lead character begins the story by doing something that will make your young reader wonder "Why is he doing that?" then you've effectively started the story with a question. If your main character just drew a picture on the wall in red crayon... then picked up a blue crayon and drew an entirely different picture on top of the first one... and then picked up a black crayon and drew yet another picture right on top of both of them... your reader is going to wonder what's going on. Now you've got him hooked!
Or, to use the "drawing on the wall" example again, perhaps your character is
drawing on the wall but NOT with crayons. Perhaps he will only draw with
a toothbrush that's been dipped in mud that he carefully brings in from
outdoors... and then only after he dumps the mud right in the middle of
the floor. If it makes your reader ask why, you're starting with a question.
Twisting a cliche is also an effective way to start a story. A cliche is more than just a saying that you've heard until you know it by heart. It's also a situation that you've seen until you know it by heart. The key is to take something basic to the cliche and replace it with something that... well, something that's unexpected. This often turns into a parody of the original.
For me, one of the classic examples is the opening to the cult movie classic UHF, where the lead character George (played by Weird Al Yankovic) imagines himself in the opening sequence from Raiders of the Lost Ark -- except he's not after a gold idol, but an Oscar. This sequence is loaded with many examples of twisting a cliche. Just watch and see if it doesn't give you some ideas...
However, here's an important point to remember when creating an opening. Your opening creates certain expectations in your reader. That "hook" needs to pull the reader into a story where the opening was important! If all those crayon drawings, one on top of each other, have nothing to do with your story, it's not a good opening for that story. The UHF opening works because that George is after a career in TV; obtaining an Oscar against all odds is the perfect hook for this movie.
Openings -- hooks -- are vital to a successful story. A well-chosen one can make writing the rest of your story much easier. Like the giant boulder in UHF, it just starts rolling and rolling and rolling until you reach the inevitable ending.