I am reframing this question slightly because I don't think the argument is a philosophical one - it sounds more like probability, and his mention of entropy suggests he is making more of a scientific or statistical argument.
I'm no scientist, but as I understand it, the second law of thermodynamics tells us that all things tend to entropy in an isolated system. Now, it is debated whether or not our universe is an isolated or closed system. Many arguments in favour of life appearing by chance rely on the premise that the astronomically improbable chance of it happening is possible because the universe is infinite, so it had to happen somewhere (like monkeys writing Shakespeare) and it happened here on earth. However, nearly everybody believes that the universe had a beginning and is expanding, neither of which make for a strictly infinite universe. It began, so it hasn't existed into the infinite past, and as it is growing it must be measurable at any given moment in time. As Douglas Adams once glibly wrote, space is just really big, but that doesn't make it infinite. The ridiculously improbable odds of us appearing by chance are then very, very real. This of course adds weight to your friend's argument. Entropy in our finite universe isn't just more likely than our spontaneous existence - its very expansion is believed to cause entropy, as stars pull away from each other working against the forces that brought them together.
Further, the difference between an isolated system and a closed one is that energy can still flow in and out of a closed system. Most agree that the energy necessary for the creation of matter from which our universe is formed must have existed before the universe itself. So, could our finite universe be expanding into something that is infinite? If so, then the chance of intelligence existing in the infinity beyond our universe is actually more likely than it existing within it - infinitely probable, in fact. And that could well be where your friend believes God, the creator of the physical universe, resides.
My point, and my answer to you, is that your friend's argument sounds more rooted in probability than religion, therefore I don't believe there is a philosophical argument that can undermine it. There are certainly other theoretical physics models and philosophies that define infinity or the origin of the physical universe differently, but these only offer alternative explanations, not counterarguments. I appreciate you've already selected an answer to your question but am happy to offer an alternative.