The
infinite monkey theorem states that a monkey hitting keys at
random on a
typewriter keyboard for an infinite amount of time will
almost surely type a given text, such as the complete works of
William Shakespeare. The chance of this happening is one in 10:500. So there would be 500 zeros. If this were the case then there would be many many many failed attempts. What happened to all the failed attempts at making a universe? Are they in the failed attempt bucket in the sky somewhere? The universe is filled with natural laws that makes it all work and nothing seems to be a failed attempt, at least on that level. Nothing failed until self awareness came along. Then people began to question if there is a God then how could he make such a mess. Even though they do not believe in God they feel this God that they do not believe in made a mess out of the universe that He created. But the same people feel that random process is doing a fine job of creation and does not make a mess at all or if it does it cleans up after itself. Still with so many failed attempts then the mess to clean up must be huge.
There are alternate ways in which infinity for creation might be achieved, and for one to be true does not rule out for the other to be true.
First of all, the universe might extend forever in all directions instead of being finite. This is easy to understand at this time, but it makes the origin of the universe conceptually difficult. Conceptually, its easier to think of the unverse beginning and continuing as the three dimensional surface of a four dimensional sphere. But this requires the universe to be finite, however great that might be in our case.
But if our universe began and remains finite though great, perhaps there are other universes that are unconnected to ours that are also finite though great. Presumably each universe could house monkeys typing away at random until one of them, somewhere in some alternate universe, achieves the works of Shakespeare.
Or we could use computers outputting tables of random numbers, and one of them accidentally recreated the works of Shakespeare doing that. Probably happens more often than teams of monkeys in the alternate universes.
Finally, we should mention the many worlds theory of quantum mechanics. According to this view, every time there is an alternate way for a quantum mechanical transition to occur, it occurs both ways, with the universe splitting into alternate universes to accomodate that happening. This would mean we have plenty of universes in which teams of monkeys typed up the works of Shakespeare.
But in any case, we'll never find them. The successful printouts that were randomly generated would be so very far apart that locating one would be an impossible task for any conceivable finite entity. We can only contemplate that such a thing does exist, somewhere, but we'll never see it.
But perhaps we don't even need to think about alternate universes. How about the infinite digits that express the square root of 2? If we look far enough into those digits, somewhere, we'll have the exact expression of the ascii printout of Shakespeare's works.
Don't expect to get there with a human created computer.