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.
We might be talking semantics. To me "random" is anything that is unplanned. So my usage of the word "random" could include events that are extremely specific and which follow strict guidelines and physical laws, as long as they happen without purposeful planning and direction.
Just because an event happened randomly doesn't mean it couldn't be reproduced arbitrarily later? Or that it would result in specific consequences, some of which would be predictable.
I see that this line of thought leads to an entirely different philosophical can of worms than the one under discussion, if taken much further.