Honestly, this is not a very good argument for the existence of God. It's an inductive argument, which means that, at best, it is only probably true. However, we cannot even easily determine how strong or weak that probability is because the evidence is very much a matter of interpretation. It is based on how things seem to be.
However, this argument has gotten some attention over the past decade or so due to the "conversion" of the now deceased Anthony Flew from atheism to theism (specifically, deism.)
In his 2007 book, There is a God, Flew describes what is possibly the one redeeming aspect of this argument.
In other words, even if every particle in the universe had been mingling together for 10 billion years, it would not have been enough time for something like DNA to come about. I suppose it could happen by chance, but not with so little material over so little time.
Many aspects of the Argument from Design are much too subjective to make a good argument, but unlike the Big Bang, the laws of physics, and the exact nature of Earth life, the origin of that life is more demonstrably improbable, if not impossible.
In addition to pure statistics, there are other issues which add to the improbability of life, such as the solubility of amino acids in water and the complexity of even a single-celled organisms DNA, which make it all the more difficult to explain, because even if organic compounds could come together, they would immediately dissolve. Even Richard Dawkins admits that we have no good explanation for the origin of life on Earth.