“We’re talking about really tiny things like proteins and RNA strands—things not even to the level of single cells. There could be lots of those forming every day (and getting eaten immediately, perhaps)—how would we ever know?”
Well, a Saturn rocket could spontaneously appear too, I suppose, but we have only ever seen those produced by human engineers and modern factories.
Similarly, we have only ever seen proteins and RNA produced by the machinery of living cells.
Okay, forget proteins for now. They've found amino acids and other organic molecules in interstellar dust and on comets. And I believe they've synthesized RNA in the lab, without the help of living cells. And there are lots of people working on figuring out the next step, to replication. Like I said, I wouldn't bet against our figuring this stuff out eventually.