There are some events in the book that show Meursault's own emotion, before he transitioned into an apathetic man. Many examples lie in chapter one during Meursault's stay at the Home. First was Meursault's decision on whether or not it was proper to smoke in front of his mother's casket. Another is during the funeral procession, when they are walking. Meursault realizes the beauty of nature that surrounded the Home and grew to understand why his mother grew to love the home and her environment. A third example is when Meursault feels the need to explain himself to his boss - and almost to the caretaker - about his leave/leaving mother at the Home all alone. He apologized to his boss, exclaiming that it wasn't his fault his mother died, as if he were guilty. These three examples showed that Meursault did care in the beginning about life. He cared enough to think about things and have a complex about them.
However, during those same events Meursault also showed signs of indifference. When his mother died, he shows absolutely no emotion from memories of her, or just the fact that his mother was dead. Since he had put her in the Home, he was detached both emotionally and physically from her. When she passed away, his life really didn't change much. During her funeral and vigil, he was indifferent. He smoked, drank, and thought of what things to do when he went back to his home,