Let’s bypass the idea that DNA, the blueprint for proteins, couldn’t come about by random chance. Perhaps the process worked backwards: perhaps the proteins came first.
That was the concept behind the Miller-Urey experiment of 1953, in which the chemicals thought to have been present in earth’s “primordial soup” (water (H2O), methane (CH4), ammonia (NH3), and hydrogen (H2)) were all combined and subjected to electricity, meant to simulate lightning. Proteins are made of 20 amino acid building blocks, and this experiment successfully produced more than those 20 (there are more possible amino acids than just those used in our own core set). This experiment was heralded as proof of abiogenesis, or the production of life from non-living matter.
There are a number of major problems with this, though. First, the amino acids produced in this experiment and in all subsequent experiments like it produce a racemic mixture of amino acids, meaning the orientation of the molecules is a combination of non-superimposable mirror images of one another. This refers to the positions of non-symmetrical components of the amino acids, whether they’re on the right or the left side (much like our thumbs on our left and right hands appear on opposite sides, as non-superimposable mirror images of one another). However, in nature, amino acids are almost exclusively in the L-form. Its opposite, called the D-form, causes the subsequently formed protein to mis-fold. Since a protein’s 3-D structure is determined by the chemistry of its building blocks, and the structure is critical to its function, this makes a protein built of a racemic mixture of amino acids non-functional and toxic to life.
This problem has never been circumvented in the laboratory. But even supposing it were, supposing the early environment beginning with chemicals in the primordial soup might somehow produce only L-form amino acids, we’d still have the information problem. Without DNA instructions to tell the body which amino acids to use in which sequence, the average length of a mammalian protein is about 400 amino acids in length. The probability of each amino acid out of 20 being placed in the correct sequence at random is (1/20)^400. If you plug odds like that into an online calculator, what you get is: zero. The probability is effectively zero. And that’s just the random formation of a single protein, assuming the orientation of all the amino acids was somehow magically corrected. A single irreducibly complex cell would require somewhere between 3-500 of those.
(And that’s not even addressing the entirely separate question in abiogenesis of “what constitutes life.” A dead body has all of those functional proteins, but they no longer do anything. Why not? What is the indescribable “something” that they have lost–and thus, what would need to be bestowed upon a spontaneously produced protein to cause it to function, even supposing such a protein could be produced in the first place?)