Yuu actually first met Minajael all the way back during the Fireworks Festival, when the group went on the trip with the Scarabia duo... It wouldn't be completely out of the question, given the set-up. Kalim's family is hosting, so it would make sense for them to invite their relatives. And why wouldn't the royals of the country show up to the event?

Minajael is stated to sneak out of the palace multiple times, causing a stir in the media in the process. What if he just so happened to be in his commoner's disguise at the same time NRC students were visiting with Kalim and Jamil??? You know, this one:

What better time would there be to explore outside of the palace than during a festival, when people from all over Twisted Wonderland are visiting and the local businesses are at their busiest? There would be so much to see and to experience!

And maybe--just maybe--Minajael bumps into Yuu (somehow separated from the NRC group, probably lost?) while he's out and about? Perhaps he's even trying to escape guards that are looking for him, and Yuu helps him out like how Aladdin helped Jasmine escape the angry merchant. Or maybe he plays the role of Aladdin? Yuu could get into some kind of misunderstanding with a merchant and BAM suddenly there’s Minajael, come to rescue them and talk them out of it.

Then they could run off together and have fun, reenact a lot of those romantic Aladdin-Jasmine moments from the movie. Minajael tossing Yuu an apple, offering a flower he picked, evading capture hand-in-hand, vaulting across rooftops Yuu accidentally stumbles and falls right into his arms, and more. Maybe they'd even open up to one another about their personal problems. Minajael feels "trapped" (in his princely obligations), and Yuu feels "trapped" too (in a strange new world). When they part ways, he's left feeling like he's made a genuine friend, a real connection.

It kinda fits for Yuu since they’re pushed by the narrative as someone who can connect with others. They feel like an Aladdin too, since they’re impoverished and live in a run-down building for most of the school year, but generally come off as a good person.

And then when Minajael comes to RSA for the interscholastic competition, he recognizes Yuu so he's automatically hitting it off with them www Yuu may not remember him, so he'd play coy and skirt around it, not wanting to outright tell them where they may have met before. Bruh, he invites them on a magic carpet ride and encourages them to hold onto him if they're scared of heights 💀

faibfuayyaeipafeib BUT IMAGINE JAMIL (whom Minajael plays against in Relic Labyrinth) SEEING THIS AND JUST. COMING IN TO BREAK THEM MAPART UNDER THE GUISE OF "it's not proper for a prince to mingle with us common folk"???? He'd even address Minajael as a prince to subtly get under his skin (fully knowing that Minajael dislikes being referred to that way). Maybe Jamil would also scold Yuu as well, either for "befriending the enemy" or "behaving so casually" with royalty.

So Jamil manages to successfully chase of Minajael for now--but right before the prince leaves, he gives a little wave and a wink, asking you to please watch his match veeery carefully. He'll show you how cool he can be!