Here are some good examples of great first impressions, other than the ones you mentioned:
Fatal Frame III. You walk into this "supposedly" (yeah, right, supposedly) haunted manor in rural Japan because you're a freelance photographer and then you see the silhouette of your dead boyfriend. You follow him to figure out what's going on, and that's when things start to get creepy. The colours become muted, there is a strange static noise, your boyfriend seems to be able to walk through walls. Then you realize it was all just a daydream.
Thing is, 10 minutes later in the game, you go to sleep and have a playable dream about that same manor. Excellent start, in my opinion.
Also, Shadow of the Colossus. There is no dialogue in the opening cutscene. Just an eagle flying over the landscape, and then you, in your house, carrying a dead woman. That's all. And that's all it ever needed.
Of course, some great games have some really, REALLY bad beginnings. Okami, which is one of my favourite games ever, had at least 20 minutes of expository dialogue before you even started to play.