Anime / Manga - Wait... In The First Episode?

Good! Every freaking show is about people falling in love, when what I want to see is a show where people are actually in an established relationship. There are like two of those.
/rant

I've seen a couple of mangas that do that. Full Time Wife Escapist has a couple that isn't together at the start, but gets together pretty early and the story is mostly about their ongoing relationship. They're also both adults and deal with actual adult issues sometimes, like him considering getting a job that is more meaningful but would require them to move and wouldn't pay as well.

Saotome Senshu is about a high school girl who's an up-and-coming boxer and her trainer boyfriend. There's a dumb, "we have to keep the relationship a secret" element but the two have really dorky, genuine chemistry.

Futari Ashita mo Sorenari ni is a very cute and lowkey manga about a couple living together. I really like this one since it focuses on all the little moments of a relationship, like picking up a little cake from that pastry shop your partner likes 'cause it was on sale.