"It was the best of times, it was the worst of times" is a lot more interesting than "once upon a time."
In screenwriting, you're taught that you have about 10 pages to hook a reader. Games carry even more of a burden when it comes to catching a person's attention in the first few moments. Given that a title typically costs more than a novel or movie, people are likely to be very selective with what they pick up and play. This is heightened by the fact that there are numerous releases to choose from every year, each requiring a significant time investment.
No beating around the bush here.
When I was a kid, I just had to press the start button to begin playing Super Mario Bros. Twenty years later, I'm playing Grand Theft Auto 4 and find myself sitting through a lengthy, largely uninteresting cinematic involving European immigrants on a freighter making vague references to the "atrocities of war" and other over-trodden tropes.
Maybe start with this instead.
If a game is going to start with a cinematic, it needs to be short, engaging, and to the point. Assassin's Creed begins with Altair jumping from a bell tower, disrupting a public execution, and disappearing from guards in plain sight as an eagle cries in the distance. That is an acceptable introductory cut-scene.
After a useful plot recap, Assassin's Creed: Brotherhood really starts with Desmond seeking refuge from the Templars and Ezio defending his stronghold from a siege. It could have all been done with a cinematic, but Ubisoft lets me run across rooftops, fire cannons, and fend off invaders. Following the obligatory opening crawl, Star Wars: The Force Unleashed lets me amputate and cauterize Wookiee limbs as Darth Vader. These are just two examples of games that get it right, at least when it comes to introductions.
That's more like it.
Some games' opening cinematics contain quick-time events to make them interactive. But as I've written before, QTEs make sense after gameplay mechanics are established, which rarely happens at the outset. The only logical conclusion is that QTEs, even ones that are properly done, have no place during a title's first moments.
The introduction of a game is more important than many developers realize. It's a crucial period when impressions are formed, and it's a perfect time to capture players' imaginations with innovative gameplay. Save the cut-scenes for the end, not the beginning.