How does a universal genetic code relate to the hypotheses about the origin of life on Earth?
Not sure of your question.
In order for life to begin on Earth, you needed information. Somehow this information needed to be inputted into the genetic code.
When Watson & Crick discovered the genetic code for life, what they bumped into was the code for information. I think one of them actually called it that. As humans, the only source we know for information-rich data is from an intelligent agent. So, in order for life to begin on Earth as we know it, some source of intelligence had to input information into a code, the genetic code.
BTW - The word hypotheses is plural for hypothesis.