Morality and purpose are emergent properties of society. They are not externally-imposed by an entity above/beyond itself (the “self” being either at the individual or societal level) any more than the organization and physical structure of an anthill is imposed by an external ant deity. They emerge from the interaction and collaboration (and sometimes conflict) between the individuals that form it.
When someone asks you what the “purpose” of your life is if you are an atheist, the perfectly acceptable answer is that (at the simplest level), your purpose is to assist in creating and maintaining an environment in which the genetic material of your overall species survives and flourishes (sometimes even at the expense of your personal genetic code). As such, it can never really be an individual, isolated purpose, since there is no purpose that is independent of defining your role and level participation in society, even if that participation is to reject it and live as a hermit. At a higher level, this translates to helping your community thrive; this, by the way is why altruism appears at the societal level, since altruism only makes sense if you assume the existence of an independent recipient.
Your “purpose” is the process of discovering what your role will be in that society, which can be something as simple as being a good father or mother to your children, or a more complex role, e.g. driving change at a large scale, where the number and nature of your relationships to the other members of the society you are affecting are far more convoluted.
In the same way, when someone asks you how you can have morals without a religious book telling you what they are, the perfectly acceptable answer is that living in a society allows you to interact with other people and understand how their actions make you feel. Because we have evolved a finely honed “theory of mind”, we can at the same time imagine how others would feel as a response to our actions. In other words, we have empathy, which is the very characteristic that has made a collaborative society possible in the first place. No empathy, no society: no empathy, no morality. It’s a very simple step from there to the Golden Rule, which was around in multiple forms centuries before it appeared in the New Testament, and can be expressed thus: when dealing with other people, always imagine yourself in their position. Strive to make that interaction a positive one. We couldn’t do that unless we had empathy.
But as an emergent characteristic, this goes both ways: yes, we can’t have a society without empathy, but at the same time we can’t have empathy without society either. We can’t have purpose with society, and we can’t have society unless our purpose is tied up in it. Morality and society are equally intertwined: they define each other, and are in a sense the different sides of the same coin, which cannot exist independently. To ask “who gave you your purpose/morality” with the assumption that there has to be an external “cause” or creator of that purpose or morality is the equivalent of asking which religious authority the ants consult when deciding the role they will have in the colony, and which holy book they read to discover how to build the anthill.
You can live a purpose-driven, moral life without a God imposing that purpose on you. All it requires is that you participate in your surrounding society: the method in which you do this is up to you. I would hope that you, as a human being with a developed sense of empathy, recognize that it is in your own best interest to participate in a positive way, to help build up and not destroy: only someone who hasn’t fully considered the consequences could think that abandoning purpose and morality is a natural consequence of no longer believing in a deity.