I think the most important elements of a story opening are to give the player a compelling hook and a compelling character to follow. The "hook" is something interesting the player will want to learn about. For example, my current project opens with the following text:
My name is Abigail. I'm a survivor.
I was supposed to get on the train that night...
But...
It didn't work out that way.
Cut to a dark alley. Abigail is out of breath and wondering if she is safe. A not-too-distant explosion and a blaring siren inform her, and the player, that she is not safe. Abigail decides to find shelter. A few steps later, an unseen creature roars, and the alley around her bursts into flames.
So here are the compelling questions (I hope) the player will have at this point. Who is Abigail? What is she running from? Why didn't she get on the train? And, of course, how will she survive whatever is going on right now?
Of course, your hook will depend very much on what kind of game you're making. Mine is more of an urban fantasy survival adventure story, so this somewhat mysterious and chaotic open (I hope) works well. Whatever you do, you'll want it to be a good representation of the overall tone of your story, and ideally introduce most of the major themes, factions, or players. That doesn't mean have the big bad evil guy show up at the front, but you'll commonly see their minions making mischief.
I hope that will be enough to get the player's attention, but what keeps me invested in a story is a compelling character. By that, I mean a character I can connect with and care about; I want to find out how they make it through whatever adventure the developer has thrown them into. That's accomplished by giving them strengths to rely on, flaws to struggle with, goals to work toward, and roadblocks to get in the way. There's no way to completely flesh all of that out at the start, in my opinion, but just like introducing the factions, I like it when storytellers will at least introduce or hint at these things.