Instead of thinking about article cases you could think about subjects and objects in English. Subjects —> nominative (direct) objects —> accusative. I give the coffee —> δίνω τον καφέ (not ο because it’s direct object.

From there you could complicate it a bit more, like subject—> direct object —> indirect object: I give the coffee to him: δίνω τον καφέ στον άντρα which then clears up why if you were to replace the nouns with pronouns άντρα becomes του not τον (του τον δίνω)

Thinks get a bit more murky with the genitive where I guess ‘s in English becomes of the, but by this point you should have it and just learn it!

Idk if that was helpful or more complicated. I found learning Greek helped me understand English grammar better in retrospect!