Hey Calliope, great question!
So first off, the Nostalgia mechanics are obviously pretty long term from initial Treasured Memory to triggering Nostalgia. At the start of your game, you could ask your players to list three Treasured Memories that their PCs already have, so that they can potentially trigger them during your game. If you're running a certain subject matter in your game that you'd like your PCs to have different opinions on, let them know that they can factor these into their Characters and their Memories.
As GM, you could also build your game's "quest" around helping an NPC or coming to a better understanding of another Character. Maybe it's not so simple as competing in an inter-school competition, but inspiring a reluctant classmate to overcome their nerves and give it their all! Maybe a couple friends are going through a tough time and your PCs have been tasked with helping them ace their test. Or maybe, if it's a more traditional adventure, the obstacles the PCs face are based on their hopes, dreams and anxieties, giving them a lot of opportunities to roleplay and discuss their feelings with their teammates. For a one-shot, you should probably only focus on one or two NPCs so that the party can forge a deep bond with them, or keep the exploration within the group of PCs themselves.
Lastly, you could pick a "quest" that has a time limit. A big test, sports match, musical performance or similar event has an in-universe start and end point. This gives the one-shot a nice structure because the players can start by learning about it, spend time preparing, then finally go all-out for the main event. When their in-universe time is up, the one-shot's over!
I hope these notes help! :)