From the given information, I find the accident hypothesis to be quite likely compared to natural selection.
Argument in favor of the accident hypothesis
Suppose the probability of finding a code more resistant (let's call it good) than the natural code in a single year is \(p = 10^{-6}\).
Then the probability that we find at least one good code in \(n\) years is \(1 - (1 - p)^n\). Trying it for different values of \(n\), we get the following

As we can see even with a million years we are getting reasonably high probabilities (~66%). On the contrary, the earliest undisputed evidence of life on Earth dates from at least 3.5 billion years ago and the age of earth being 4.5 billion years. Which leaves us with a period of 1 billion between the two. This highly favors the accident hypothesis.
Assumptions
I assumed that genetic codes are generated each year uniformly at random. This need not be necessarily true as there can be other factors which affect the generation of codes.