I am suggesting that while the organic compounds may have had to follow specific laws in order to form DNA/RNA, the events themselves during which those laws were followed with those results were random.
Well, if you consider the large amounts of the various elements in a high energy environment such as when the Earth was forming, great number of organic compounds would form with increasing complexity.
Dr. Stanley L. Miller performed a classic series of experiments using water, hydrogen, methane, and ammonia (present in Earth's early atmosphere) in which an electric current was introduced briefly (such as from lightning in early Earth) and he collected the resulting compounds. He found amino acids, building blocks of proteins and DNA, among the compounds.
If it can be reproduced, it becomes difficult to fit into my definition of random.