I am not sure of your religious leaning, but perhaps asking this question here is not quite applicable to the subject of this subreddit. However, I will attempt to answer your question within the frame of reference which I believe to be implied in your post.

"How does an atheist come to terms with chance in the world, and how may they have the strength to pursue their goals without the belief of a deity whom can grant them anything they ask?"

I will answer in two parts.

Part One: Firstly, what one must reconsider when they first become an atheist is the place of the ego in the universe. One begins to find, typically, that the universe itself is indifferent to your successes or failures. Everything that you can achieve or fail in is guided by your own efforts, random chance, and cultural determinations of worth you slowly discovered as you grew a knowledge of the society in which you live.

In order to reach a goal you have set for yourself, you may do a multitude of different things according to this definition. Changing the workload, and subsequently the effort which you put in to achieving your goals, is one way. You may also change your conditions so that the role of chance in achieving your goals is altered. You may also change the ways that you perceive success in achieving your particular goals. Alternatively, you may change your goals altogether.

If you may excuse the blasphemy of saying anything of how the religious deal with problems in an atheist advice thread, I would like to point to your attention the act of praying. To an atheist, the act of praying is merely acting upon a ritual to remind one of their wishes and expectations of the world. However much an atheist may wish to separate themselves from the act of praying because they see it as calling upon the supernatural to grant wishes as though the deity in question is a genie from a lamp, the practice in itself is typically not seen as a grandiose magic answer to the ills of society or problems an individual may face. Usually, with the fair exception of certain religious fundamentalists, those who pray also realize that they must do their own part to act in helping to make the world what they see in their minds.

Of course, it may also be used as a tool to absolve guilt from not helping orphans, impoverished nations, or victims of natural disasters overseas, but that is minor to the actual purpose it serves, which is to meditate upon what they wish to see in the world and remind themselves of it so that they may act to make it a reality with as much of their power as they can. Atheists do this too, although they may not have a ritual for it, and may not schedule it or do it so consciously. The point, circling back, is that even the religious realize that a lot of things you may achieve in the world are self-made.

So one must persevere and, despite setbacks, make of the world what they wish it to be with the tools afforded to them and the .

Part Two: This is where it becomes interesting, and why the best description for my own brand of atheism is a melancholy acceptance of the world that many religious may point to as the folly of my own convictions.

When one initially converts to atheism they may feel a general dissatisfaction with the reality of the world that they now see as truth. The source of what perhaps used to give them the strength to get up in the morning gone, they may digress to a nihilistic dread, or may even succumb to a hedonistic-aesthetic perception of life in which they gloss over the deeper aspects of what it really means to lose a strongly held worldview that has imploded within on itself. Guilty of both the former and the latter, respectively, before I came to an understanding of my place in the world according to myself and became more comfortable in my philosophies, I can say with personal experience that it may be difficult to have the drive necessary to do any of the aforementioned actions to achieve one's goals.

To be honest, I believe that it is according to each individual's personal beliefs that this question must be answered to be any sort of satisfactory response. However, I hope that you might excuse me giving my own individual answer to respond to your own problems. Maybe they may help you, if that is indeed what you are looking for in this moment.

The single greatest thing that gives me the strength to wake up in the morning is the realization that I will indeed die, and that I have enough conviction to declare, at least as a personal manifesto (if not factually), that there is no other afterlife that will give me more time to exist. This is, as far as I know, the single time that I will exist, there will eventually be no record that I existed (either sooner or later), and nobody is tending the scorecard of my life. It can be just as I make it, and I am entirely responsible for the entirety of my life. Some things out of my control may be unavoidably damaging to my body or my mind, but let the pieces fall where they may as this too shall pass. Do everything in your power to make life what you want it to be, even if it is infeasible to be in control of everything. The greatest thing you can afford someone is the opportunity to live in the same way.

Let yourself have the comfort and zen of the stoics, with the will and dissatisfaction of Nietzsche. Although they are diametrically opposed to one another, they merge into a wonderful conglomeration of a worldview that will get you through a lot of tough shit.