That is at least plausible. Look at a chaotic explosion and you'll find at least some orderly patterns within it. It's the argument that if you put a near infinite number of chimps on typewriters or put one chimp on a typewriter for a near infinite period of time, sooner or later one of Shakespeare's plays would be typed. If you had that play in your hands, you might very well think it was typed intentionally, but it was entirely random. You couldn't even prove randomness or intention with statistical analysis, because that play could have been the first thing typed (highly improbable but not impossible) or produced after billions upon billions of years of typing.
The problem is that such arguments rely on actual infinity and properties of the random distribution which may or may not hold.
The universe, while large, is finite, and of finite age. Arguments that ordered arrangements must arise in random (or arbitrary) structures of sufficient size are the domain of a part of mathematics called Ramsey theory. It turns out that the sizes of structures needed to guarantee ordered arrangements of even simple sorts can be staggeringly large (look up “Graham’s problem” and “Graham’s number” for an example). It is not at all clear that the old “the universe is so old and so big that life would have to arise just by chance” argument is actually valid.
"billions upon billions of years of typing." there has not been enough time for all the chips to fall into place to have the diversity of animal, flora, and insects that this world holds.
I heard a theory that possible microbial life came here from a comet or asteroid. Well if that was true then the moon should have more life than any place since it has so many pock marks from asteroids hitting.
Even moreso is considering organic chemistry. Yes, it’s incredibly improbable that you can form DNA from what? Again, this isn’t to say that we can’t synthesize incredible chemical compounds from base materials such as sugars or petroleum, but all chemical syntheses require incredibly strict, step by step control of the chemical reaction to work. Even then, you have to sort out what is the genuine product, and what are the isomers. All I am saying is that yes, some things are just rediculous to try and leave it up to saying a random origin produced it, organic chemistry is only part of it, too.