To invoke the origin of the DNA/protein machine by invoking a supernatural Designer is to explain precisely nothing - for it leaves unexplained the origin of the Designer.
My computer is a very complex gadget and it was designed by many designers, so why must the universe have only a single designer and not many designers?
However statistically improbable the entity you seek to explain by invoking a designer, the designer himself has got to be at least as improbable. God is the Ultimate Boeing 747
You can't statistically explain improbable things like living creatures by saying that they must have been designed because you're still left to explain the designer, who must be, if anything, an even more statistically improbable and elegant thing.