The search space is highly constrained. All life on this planet is based on hydrocarbon chemistry, more or less, and must operate in the face of high rates of oxidation and water as pretty much the only available solvent. Even with such constraints, the differences between what has evolved (bacteria to blue whales! viruses to polar bears! algae to orchids!) are staggering.

The fact that you find something hard to believe doesn't say much at all. Humans have all kinds of things that we find hard to believe - for example, I find it almost impossible to believe that there is only one object I can see in the night sky with my own eyes that is outside of our galaxy - but that doesn't make them any more or less true.

Let's take human DNA as an example. It contains 3.2B GTCA base pairs. This gives rise to 4^3.2B possible combos. It's just not possible to navigate this space blindly. There is not enough atoms in the universe to do that. It is known that there is bias in what mutations are favoured.