@janik.schiller Per my understanding, the original argument was not about the existence of our universe, but rather the origins of complex life forms. The original argument assumed the universe existed, if I understand correctly, and that given infinite time and chance beings such as us would inevitably exist. To apply this argument to the existence of the universe is a modification of the original argument and, in my opinion, invalid. Before the universe existed, what was there? Where did that come from? We ultimately have to posit something that is eternal. Even if there was a little universe generating machine being run by a galactic monkey, where did that machine come from in the first place? So the question of origins of the universe is even harder, which is saying a lot, than the origin of life.
I honestly cannot speak to the accuracy of Schroeder’s math, since I have not double checked it myself and I am uncertain about the exact age of the universe posited by scientists, but I think the argument holds even if you continue to increase that age many times over. The principle he is trying to communicate is much more fundamental. Reason does not spring into being from non-reason - information always has its source in an intelligence. If we find a cuneiform tablet with fifty years of financial transactions for camels, crops, etc. buried in the ground, we do not go - wow, look at what chance produced. Rather, we immediately assume it was produced by an ancient civilization. Monkeys do not produce sonnets or cuneiform tablets and time and chance does not produce intelligent life.
But I think you asked another question - how do we respond to a person with this objection? I think each situation is different and we need to remember the goal is not to win the argument, but to share God’s love and truth with the individual. So even as we share these ideas, I think it is important to listen and to understand their perspective at a deeper level as we pray for them.
Are those thoughts helpful?