https://en.wikipedia.org/wiki/Orotidine_5%27-phosphate_decarboxylase This enzyme causes a reaction that would ordinarily take 78 million years take 18 milliseconds. It seems this enzyme is needed to make pyrimidine which is needed to make DNA. Also, I think DNA is needed to make the enzyme. But I have a very basic knowledge of chemistry – perhaps there are other ways that DNA can be made, without pyrimidine, or ways to make pyrimidine without the 78 million year delay! So do you think this adds to the extreme unlikelihood of spontaneous abiogenesis?
Almost by definition, DNA cannot be made without the production of pyrimidine molecules. Two of the four nitrogen-containing bases which form the backbone of DNA are pyrimidine molecules. I am not up on this particular enzyme, but this is more or less typical of all enzymes, that they increase the rates of otherwise non-spontaneous reactions by millions or even millions of millions-fold. So, for the sake of argument, I will assume that this claim is true. If so, then this is just one of literally thousands of examples of a reaction which would, in principle, have to happen in order for a living thing to be created by spontaneous reactions which are, in fact, not spontaneous. The general picture is that in order for proteins to be made, it is essential that DNA exists, and in order for DNA to be made, proteins must exist. So, neither can exist without the other. It is kind of like a biochemical chicken and egg problem. The one you give is an example which shows that DNA cannot exist without a protein being in place which could catalyze the creation of DNA. Yet this very delicate and intricate protein could only be made using the information carried in DNA.
I would have to do some research, which I cannot do now here in Nigeria teaching for a church, so I cannot guarantee that there is no natural process by which pyrimidine can be made spontaneously, so I want to be a bit careful to say absolutely that this particular enzyme is required, but I do know that there are literally hundreds of examples of reactions which only happen with the help of enzymes to catalyze them, yet the enzymes themselves required cannot be spontaneously assembled without the information contained in DNA. So, I absolutely agree with your general thesis that the existence of life represents a problem which is literally impossible to answer by simply proposing natural, spontaneous processes, operating outside an existing intelligence. This is a very strong argument for the existence of an intelligent supernatural Creator of life. Thanks for your question and for your example of this principle.