the game is saving at certain check points - and in the intro mission, which you are playing currently, you cannot save the game even in non-survivor mode. It is actually a quite short intro mission and a little training in hunting game is not bad. You have a safe environment where you build your bow and hunt those goats, use it to gather other materials, in this safe area before you move on. During the intro mission that campfire and other locations will be a check point and you will start there again, if you fail, but when you quit the game, you start at the beginning of the mission.
Later in the game, if you use the save & quit option, you will start out at a respawn point again, it is not bringing you back to the same location in the world, if that is not a respawn point. Well, I do not want to say more about it, don't want to spoil it for you.
The intro mission ends when you discover the land of Oros - there it is safe to quit the game.