The current alternative to the "problem" of anthropic coincidences is the multiverse theory. Anthropic coincidences at the universe's beginning strongly suggest that our universe has been fine-tuned for the existence of "anthropos"; i.e., you and me. Talk of a "fine-tuned" universe implies there is a fine "Tuner." Now note: atheists acknowledge the fine-tuning problem. It's a problem for them because it's really, really hard to believe that we just lucked out in a most highly improbable manner.
So the atheist then suggests that our universe is only a part of a near-infinite "multiverse." That is, on the multiverse theory, there are (supposedly) an unimaginable number of universes (some say 10 to the 500th power).
But the existence of other universes cannot be empirically verified. Just as certain scientists argue that Intelligent Design theory is not "science" because it cannot be empirically verified, the multiverse theory appears not to be "science."
Leonard Susskind, professor of Theoretical Physics at Stanford University, is a proponent of the multiverse theory. He was asked in an interview, "If the multiverse theory does not work out are we then left with intelligent design?" (Or, the existence of a "Tuner" on the basis of our exquisitely fine-tuned universe?)
Susskind replies: "I doubt that physicists will see it that way. … I am pretty sure that physicists will go on searching for natural explanations of the world. But I have to say that if that happens, as things stand now, we will be in a very awkward position. Without any explanation of nature's fine-tunings we will be hard pressed to answer the ID critics. One might argue that a hope that a mathematically unique solution will emerge is as faith-based as ID."
The fine-tuning argument is also referred to as the Anthropic Teleological Argument. I see it as a powerful argument for the existence of God. For one statement of this argument see William Lane Craig's essay here.
