It's hard to help without knowing your team but generally yes leveling up is essential, and not evolving them until you can fit them on your team is also essential in the early game.
The new quick results thing is SUCH a great improvement. Damn, what an update.
I mix up my team to fit with the dungeons, but my main players are:
Incarnation of Suzaku, Leilian
Burning Maiden, Princess Valkyrie
Sleeping Dragon Zhuge Liang
Drawn Joker
Keeper of Rainbow
For some high star monsters I don't use much, I have:
Red Knight, Nim.
Shaitan, The flame elemental.
Shiva
Archangel Raphael
Radious
Undine, The water Elemental
Other than that I have some color Ninjas, a samurai Ogre, some drops from Collaberation dungeons that don't seem all that useful, Cerberus (Who has negative recovery for some reason), and Dark Golem MK.II.
I'm trying to even it out so I have better middle tier monsters, but I'm just not finding those drops. But I also don't know where to look.
Welcome to normal dungeons, enjoy your stay
There's always the workhorse resist or 4/1/4 teams you can build which grind through those dungeons very slowly.
With the update to 7.8.1 we'll also start eventually seeing the tamafatty dungeon, which at your rank will instantly give you ~10 ranks with absolutely zero risk.
We're getting the Hello Kitty collab again soon, which are pretty easy dungeons with a high rank EXP/ stamina ratio.
Good to hear things will improve. But what's a tamafatty dungeon?
And I read something about feeding Carbuncles before feeding them to another monster. How exactly does that work?