You can’t catch it, and the game doesn’t have Quidditch
We knew Hogwarts Legacy wouldn’t have Quidditch for some time now, and the game even tries to justify its exclusion with a bit of lore. You can, however, spot the Golden Snitch in several ways, even if you can’t catch it.
The Golden Snitch can appear in the main loading screen
Before you load up a character, and before you’re actually in the game world itself, the Golden Snitch can make a brief cameo appearance.
It’ll flitter by and briefly interact with your character, who will attempt to catch it: to no avail. That’s pretty much the only “reliable” way to actually see the Golden Snitch in Hogwarts Legacy, but there is one other scripted brief appearance in the core game.
The Golden Snitch also makes a break appearance in The Room of Requirement quest
During the quest to unlock The Room of Requirement (which is a main story mission), you’ll encounter the Golden Snitch briefly. A Golden Snitch will also appear as an Easter Egg during this sequence, leading players to another path with a treasure.
After that sequence, the Golden Snitch is gone forever: unless you can spot it in the loading screen again. Hopefully Quidditch will arrive in a post-launch update, or in a potential sequel, so we can actually have the satisfaction of catching it.