glimpse
A very quick, partial look at something.
A glimpse is a very brief, incomplete look at something, usually because you see it for only a moment or from a limited view. When you catch a glimpse of a deer darting through the trees, you see it just long enough to know it was there before it disappears. When you glimpse a friend's face in a crowd, you see them for only a flash before other people block your view.
The word suggests something quick and partial: you don't get the whole picture, just a snapshot. A scientist might get her first glimpse of a rare bird through binoculars, seeing it for just seconds before it flies away. A reader gets a glimpse into a character's thoughts through a brief memory or confession in the story.
Sometimes glimpse means understanding something partially or temporarily. When you suddenly glimpse how a tricky math problem works, you see the solution clearly for a moment, even if you can't quite hold onto that understanding yet. This is why people talk about glimpsing the future or glimpsing what's possible: they mean catching a quick, incomplete view of what might come, like seeing a few frames from a movie instead of watching the whole thing.