About a year ago, there was this light novel I read and now I can't remember it. It's about his kid who was sent to another world with his class and during a dungeon run, he sacrificed himself to help this girl. He falls in a pit and there he discovers a dragon god or something.
This could be Arifureta: From Commonplace to World's Strongest, though it is a bit off from the manga at least. I haven't read the light novel version, so it might be because of changes between the adaptations.
The main character's class was summoned to another world. The kingdom that summoned them sent them into a dungeon for some training. During the training, a monster from the deeper levels of the dungeon got summoned to the floor the group was on. The main character then acted as bait and distracted the monster while others were fighting it. They defeated the monster by destroying the floor below it, so it would fall to it's death. Someone hit the main character with magic, knocking him into the hole.
After surviving the fall and finding a safe spot, the main character grows in strength and eventually finds a woman sealed in the dungeon. He frees her and fights the monster that appeared after breaking the seal. The woman turns out to be a vampire and they continue through to the end of the dungeon. The creature they fight at the end is not named, but can be described as a hydra or a multi headed dragon. After they fight they find a room that contains information about the dungeon, including that it's purpose is to grant people the power to strike at the gods.
A few things to note, in the manga it isn't mentioned that he is acting as the bait to protect a girl. However, there is a female friend in the class who seems to have feelings for him, and is saddened by his 'death'. This could be portrayed differently in the light novel, since we don't see the main character's thoughts while this happened. The main character didn't exactly sacrifice himself, as he was pushed into the pit, but he seemed to accept there was a chance this might not work and he would die. In the pit he doesn't discover a dragon god, but he does find a monster that could be a dragon and information about the gods.