By evolution from a simpler and less efficient enzyme. Mutation, followed by natural selection.
OK, the amino acids form (happenstance)
In the conditions believed to exist in pre-biotic Earth (very unlikely happenstance)
In proximity (happenstance)
To create a enzyme (happenstance)
Which survives, multiplies and evolves into something that uses polymers of nucleotides to code for polymers of amino acids (miracle).
It is irrational to believe in miracles without believing in God. Why not just believe in God?