Once upon a time, there was a small-town couple who wanted a child. But they were told by doctors that they could never conceive. And so, one night, as a way of getting over their disappointment and getting on with their lives, they wrote down on scraps of paper every wonderful thing they ever wanted a child of theirs to be — “Honest to a fault!” “Picasso with a pencil!” — and then placed the notes in a wooden box, which they buried in the backyard.

And then they went to bed.

But later that evening, they were roused from their slumber by the arrival of a visitor — a little boy who had magically sprung from that very spot in the ground where they had planted the box. Indeed, he bore leaves on his legs, not unlike an exotic plant in bloom. The couple took him to their hearts, and named him Timothy, and swore they would raise him as their son.

But they did not know that they would have him for only a little while.

And that, my friends, is the story of The Odd Life of Timothy Green, an affecting and enchanting bittersweet dramedy set to open Wednesday at theaters and drive-ins everywhere. I have no doubt whatsoever that some of you already have decided, after reading this far, that you will avoid this modern-day fairy tale like the plague.

But if you can get past any instinctive cynicism about sentimental cinematic fables, and accept this heartfelt movie on its own terms, you may be in for a moviegoing experience that truly is, well, magical.

Joel Edgerton (Warrior, Animal Kingdom) and Jennifer Garner (13 Going on 30, TV’s Alias) star as Jim and Cindy, the couple eager to start a family, while newcomer C.J. Adams plays Timothy — and Odeya Rush makes a most promising movie debut as Joni, a wise-beyond-her-years classmate of the newly sprouted flower child.

And by the way: That’s not exactly a spoiler back there. Much like many makers of classic films noir used first-person narration to underscore the implacability of fate and the unavoidability of outcomes, writer-director Peter Hedges (Dan in Real Life, Pieces of April ) frames most of Timothy Green with an interview between the aforementioned couple and representatives of an adoption agency — so that, right from the start, we know that this story may not necessarily end with happily-ever-aftering.

But it’s a charming story nonetheless, told with the same seriocomic sensitivity Hedges brought to his screenplays for What’s Eating Gilbert Grape (which he adapted from his own novel) and About a Boy. Along with Edgerton, Hedges visited H-Town a few days ago to talk about Timothy Green. Here is some of what they had to say.

CultureMap: Peter, at what point in the scriptwriting process did you decide, OK, this is a fable, so while I have to be logical, I don’t have to be realistic? That is, when you decide you didn’t have to explicitly tell us things like how Cindy and Tim explained the sudden presence of Timothy, or how they could register him in school without a birth certificate of some sort, and so on?

Peter Hedges: I understand what you mean. And the very first draft of the movie dealt very overtly with some of those issues. But as I rewrote and rewrote and rewrote, some of those things fell away, because they didn’t feel as important. There still are things in the final draft that I hope will satisfy the majority of people. But, of course, there are some people who are never going to go with this kind of premise.

It’s just that, well, I remember when I was doing What’s Eating Gilbert Grape with [director] Lasse Hallstrom. I was writing the love story, and Lasse said, “There are certain things that are true about love stories on film where you can take certain short cuts. If you were going to try to reinvent every moment all the time, this thing is going to go on forever.”

So I’m banking on the good will of the majority of the audience. But on the other hand, we do have the people who are interviewing the parents saying, “You do know that we are going to check out your story. And if it doesn’t check out . . . ” And Cindy says, “Good. We hope you will.”

Now that may not be enough for some people. But ultimately, is this story about a boy coming out the ground with leaves, and convincing people that it really happened? Or is the story about a couple who really want to have a kid, who get a kid for a magical period of time, and that ultimately leads them to having the kid that they’re supposed to have?

Joel Edgerton: It’s sort of like you’re handing over one thing that’s risky in order to get a lot of return. If you ask people to suspend their disbelief, and sort of turn a blind eye to certain little things — the benefits are great if you can get away with it. And if you’re not met with too much cynicism.

CM: But Joel, what sort of challenges did that place on you as an actor? When you’re trying to figure out your character’s motivation, don’t you usually find yourself asking the same questions an audience might?

JE: Absolutely. But imagine a situation where the only research you’re allowed to do as an actor is reading the script. It’s like there’s some sort of ban on you searching the Internet, or going to the library, or talking to real people that something like this happened to. All you can do is read the script, and that’s all the information you’re going to get. Well, that is a good project.

Because if a writer’s done their job, the world of the film exists in the pages that you’ve got. And it extends beyond those pages through your own imagination while you’re reading it, and through the writer’s elegance while they’re telling that story. For me, it was enough just to invest in that suspension of disbelief with Timothy Green, and not question it too much.

You know, it’s really interesting that you ask that question, because there never were times when I felt as an actor like there were scenes missing. Or times where Jennifer and I haggled over the possibility or the plausibility of this stuff we go through with Timothy and his leaves and his origin. Because I felt like Peter had done so much heavy lifting early on by making it so clear how much this couple really wanted a child.

And how this desire to become a real family was going to mean [our characters] simply were going to accept the impossible in a way.

CM: In a way, the overall look of the movie makes it easier to accept this as a fable. It’s not exactly what you’d call magical realism, but it’s not hard-edged reality, either. And it’s actually film, not digital video, right?

PH: Yes. And it’s funny: It’s gotten so rare for people to make films with film that when the crew came on the set for the first day, John Toll — who’s our director of photography — he had the mags up and the cameras out, and the crew would kind of just come in and pet the camera. They’d just say, “Film! Film!” That was fun.

But when we had talked about it beforehand, Disney has said, “We think you should shoot it in digital.” And I said no. And they said, “We really think you shoot it in digital.” And I said, “We’re not going to hire John Toll, arguably one of the greatest d.p.’s who walks the earth, to come shoot digital for the first time. This is a movie about people. And what captures people better than film?”

Look, I shot a film on video, and it was a good experience, so it’s not like I’m against it. But there is something special about film — you feel it. I feel it.

JE: I just feel that you should have the right format for the right subject matter. If you’re lucky. When I come to a project, quite often I’m asking questions about not just who’s involved and the script and all those things. I also ask how much money it is being made for.

Not because I’m worried about my slice of the pie so much. But, like, if you tell me you want to do an asteroids-hitting-the-earth movie, and you’ve only got $4 million to do it, I want to know that you’re affiliated with a really amazing special effects company. Having the right money for the right story in the right format is just as important as who you’re working with.

CM: Obviously, Disney wants to promote The Odd Life of Timothy Green as very much a family film. But how old do you think a child should be before he or she sees it? Ten? Eight? Five?

PH: Five is probably too young to understand this movie. For me, the secret of the movie is, it’s a movie made for adults that they can bring kids to. I never pictured it as a kid’s movie. Although I have to say, I have been struck during screenings where families have come with 9-year-olds and 13-year-olds. And that experience for them has really been fun to watch. And I noticed the kids really identifying with C.J. and Odeya.

But what I hope for parents while they watch the movie is that they become increasingly cognizant of the limited time we have with our children. I don’t think we can be told that enough — that they’re growing up quickly, and you only get kids for so long.

This was never made more clear to me than the time my wife was having an argument with my older son. See, he wanted to go away on a weekend with some friends. This was right before I jumped into this, to try to make this movie.

And she said, “Well, we’re going away as a family.” And he said, “No, I want to be with my friends.” We didn’t know what to do, because this was the first time he was really being willful. He just really dug in.

So finally, Susan, my wife, took a piece of paper, and wrote a zero, and then a 90. And then between them, she put a 15, and then a 30. And then 45, 60 and 75. And then she said, “Simon, this is how long we hope you’re going to live.” But then she drew a line where there would be 18.

And she said, “This is how long we get you.” And then she drew a line back at 15 — which is how old he was. And she said, “This is how much time we have left.” And my son, who’s a boxer, who does yoga, who could crush all of us in this room — except for Joel. No one crushes Joel. But tears came to my son’s eyes.

And he said, “Yeah, mom. I’ll go with you on the weekend.”

So I wanted to make a movie that reminded me and reminded other people about the preciousness of time. And how little time we have left with our kids.