DNA works similar to computer programming code.
No not really. It is a metaphor for DNA nothing more.
As in the OP post, what came first the chicken or the egg...intelligent life using DNA as a programming code for all life forms on Earth.
That isn't the question in the OP. It is about replicators or protein.
Simple replicators came before intelligent life obviously.
There was an interesting article a few weeks ago that looked at it from the point of view of physics. It took the perspective of living things as local and temporary systems that find efficient ways to capture energy and defy entropy. It showed how life is seems to be inevitable.