You can do the same selfless acts that a Theist can do and even more if you determine to, but can you really be selfless? You may say as another Atheist said,
Can you explain why my disabled, unemployed friend, who is a Christian, can’t find anyone to help him move his belongings from his storage unit to his house, so I, an atheist, am going to borrow a truck and spend a second day, (a day that I desperately need to be working) moving stuff for him?
There’s a bit of pride and selfishness in this oddly self-serving statement. Notice how this man’s “I” is better than the “I” of the man who’s not helping to move the man’s things. Self is magnified here when it should be diminished. Selflessness actually takes more than most of us are willing to give. A man may serve another man and be selfless in his acts, but selflessness goes beyond acts. It means that your “self” is abandoned in order to promote the “self” of another. Your “Self” or “Identity” is lost in the process. Who you are means nothing compared to the person you are serving.
But, why would you give up your “self” for another human being that is just as flawed you? Each man is just as capable of lying, cheating, stealing, murder, rape, and abuse as every other man. None of us are prefect. Why would you, as a flawed man, lose who you are in lifting up another flawed man? Certainly, it is good for mankind to serve one another, but the only selflessness that is worth practicing is toward a perfect individual. Therefore, I conclude that losing my “self” to the “self” of God, who is perfect, is the only worthwhile selflessness worth practicing.