this is kind of a weird one but percy and athena for the ask game?
Oddly enough, this is one I've actually thought about before, and it was an Apollo/Percy fic of all things that set me down that path.
I have a few ideas for them actually, but something about Athena that works well here is that for her, it's more about working toward something with someone. Working together on some sort of project, picking someone's brain, etc. Percy's smart, okay?
Anyway. Percy and Annabeth are besties, but Athena is still doing her "you need to stop hanging around with that boy" disapproving thing, and sure, Annabeth might not have the best relationship with her mother, but Athena's around enough for this to get Annoying. So Annabeth reaches a point and is like "you know, he's not nearly as bad as you think he is. If you actually talked to him once you'd know that."
Athena doesn't believe this at all, but she is curious what has her daughter so determined about this. For now it's some handwavy explanation, but Athena shows up and sees Percy working on some sort of project -- hell, maybe it's plans for a New Athens type thing for the Greeks since the Romans have New Rome -- and all of a sudden, Athena gets distracted by the project. She ridicules Percy immediately, of course, points out everything wrong with it, but Percy is able to shoot right back and hold his own in the discussion.
And, well, at some point, Athena finds herself invested in the project and in Percy. At some point, there's a brain baby because that's what Athena does and that's a weird moment for Percy and Annabeth but you know what? Vibes.
// Send me any two characters, I'll tell you how I'd get them together