Specifically, how can believers claim that God is the sole Creator of everything that exists, is all-knowing, is always present everywhere, and is also completely and uniquely Good — when there is so much Evil in the world?
The problem is thousands of years old, but I think the most entertaining statement of it is given by Monty Python in their memorable parody of the Christian children's hymn, All Things Bright and Beautiful:
Whatever else you can say about living in this Universe, it is simply the case that sh_t happens. You can even classify religions according to their Hermeneutics of Fecal Occurrence. Evil, in its natural (e.g., disasters, diseases, pain) and moral (e.g.,violence, crime, discrimination) varieties is woven into the fabric of our reality. If God is the ultimate source of everything that exists, isn't that ultimately God's doing? Does the existence of Evil mean that either God is not completely Good, or that God does not exist?
Having stated the Problem, let's make some observations from which we can ground our reasoning. The first one that I can think of is that it is possible for atheists to lead enjoyable and fulfilling lives, and die peaceful and dignified deaths. You can get through your entire life in this Universe without reference to any God, gods, supernatural influences or religious experiences of any sort.
Three hundred years of modern science backs this up and takes it a step further: All the progress science has made thus far has come about by scientists (even those who have been religious believers) avoiding the hypothesis that God is the immediate cause of this or that, and proposing some other immediate cause instead. Not only is the hypothesis of God unnecessary — in some contexts, it's a hindrance.
We might therefore accept as an axiom that the Universe is such that we are free to live our lives without reference (or deference) to any concept of a God, gods, or divinity.
For religious believers, this appears to be God's Will. On to part 2.