For the time? A New Hope. Opens with easily the most impressive spaceship battle ever filmed, moves to an exciting battle, introduces an awesome menacing bad guy ("If this is a diplomatic ship, then where is thr ambassador? breaks neck with one hand and throws away the body) and kickstarts the plot.
Children of Men (2006) sets the scene perfectly: the future is filthy, the youngest person on the planet has just died, and our protagonist just narrowly survived a terrorist act. Marvellous film.
Saving Private Ryan is my pick but just to add something new to the conversation I’ll add Catch Me if You Can for one of the best illustrated opening credits.
The Dark Knight - great IMAX-shot visuals, amazing atmosphere and music, action right out of the gate. Sets the tone that the Joker is one crazy mf'er while being basically an entire heist movie in a few short minutes.
Star Trek: Into Darkness - The first 10 minutes is my favorite demo sequence of all time. COLORS are really vivid and make the alien world look actually, well, alien. Good audio effects with spears whooshing by and water falling off the ship. Really nice cinematic shots of the Enterprise and the volcano. Ignore what the characters are saying (because it's all dumb) and stop watching the movie after the alarm clock goes off, but everything else is about the best thing you can watch on a really nice home theater setup.
Not quite the FIRST scene but I've always really liked the opening sequence of Fear and Loathing in Las Vegas where they're driving through the desert.