If you have an infinite number of monkeys with an infinite number of typewriters they will make an infinite mess.
Infinite is so large that they would also create perfect order and perfect roast chicken. So big is infinity that an infinite mess would be considered perfection at some point.
No, IF you truly had an infinite number of monkeys with infinite time you would eventually get every possible text in existence. Your text:mess ratio would be on the order of 1:∞ but any text you want would still exist somewhere in the mess. That is the main concept behind infinity and the monkey theory is valid with those assumptions.
Of course we don't know two things that may never be proven:
-Is the Universe infinite?
-Was the time taken to create the universe infinite?
IF we do prove these things, random creation of life in our reality is a reasonable theory. Of course it still doesn't explain the mechanics of the universe, how matter/energy began and the concepts of consciousness, time, etc.
IMO:
-The established mechanics of the Universe (time, matter, energy, gravity, etc) are where the higher power can be "seen" within the reality we perceive.
-Everything we perceive, including all life, is the seemingly "random" result of these mechanics.
-Science will someday conclude everything as "random". And they are correct when looking at everything from our perspective.
-Our limited perspective will never allow us to understand the higher power that created the universe or why it exists. After a lifetime of going to the ends of the earth to find out, I'm convinced that the "answer" is not something that can be expressed here by anyone. It has been SEEN by many people throughout history and summarized as "God's Word" but they can never truly describe it all to another person with the tools that exist here.