Hmm... casting a spell without a spell slot, nor a magic item designed for it?

That's gonna be an impossible task in most situations. I could see a case where someone else is providing you the spell slot - the power to do the casting - somehow (I leave that mechanic up to the player asking to do it). And then the INT (Arcana) check would be to see if you've watched enough of your friendly neighborhood wizard in how to actually conjure up that little bead of doom.

In my personal homebrew campaign word, magic is just code to influence quintillions of nanobots that actually form the effects. Wizards learn the code; sorcerers inherently know how to manipulate it, etc. A Fighter could conceivably steal someone else's datapad and release the code that generates a fireball - but without the right key to let the nanites know you're a codeworker, they'll wreck havoc on your system, yanking the energy needed to form that ball of fire.. essentially, dealing as much damage to you as the fireball does to someone else. I suppose an Arcana check could be used to try to fake the key... but it likewise would be nigh impossible. A DC 30 at least. YMMV.