Could a complex eye like ours really evolve one small step at a time?

Yes, and Darwin himself showed why it isn't impossible. In On the Origin of Species, in 1859, he admitted that the eye evolving by natural selection seemed, at first glance, absurd in the highest possible degree, echoing the philosopher William Paley, who in 1802 had called the eye a miracle of design. But Darwin laid out the escape hatch: if a chain of small gradations connects a simple, imperfect eye to a complex one, each step useful to the animal that has it, and if those variations are inherited, then a complex eye built by natural selection is not ruled out, however hard it is to picture. He sketched a stepwise path, from an optic nerve merely coated with pigment up to a moderately sophisticated eye, and pointed to living animals as examples of the stages in between.

The fossil record fits that picture. The oldest certain fossilized eye, found in Estonia and dated to about 530 million years ago, already looks much like the compound eye of a modern dragonfly or bee, just with its individual light-sensing units spaced farther apart and missing a lens entirely. By the time of the Burgess Shale, not much later, a striking diversity of eyes had already evolved, and complex, image-forming eyes are now known to have evolved independently more than once across different animal lineages, rather than being invented just a single time.

This sudden flourishing of eyes lines up with the Cambrian explosion, the burst of rapid evolutionary diversification seen in the fossil record. One proposed explanation, the 'Light Switch' hypothesis, suggests that once advanced eyes evolved, they kicked off a predator-and-prey arms race that accelerated evolution across the board, since before that point, animals may have sensed light without yet using it for fast movement or visual navigation.

The strongest answer to Darwin's own doubt, though, is mathematical. Scientists have tried to estimate how long it would actually take a patch of light-sensing cells to evolve, step by tiny step, into a fully functional vertebrate eye, based on rates of mutation, the advantage each step gives, and natural selection. Even overestimating the time for every stage and assuming one generation a year, the answer that comes out is startlingly short: less than 364,000 years, a blink of an eye, so to speak, on the scale of geological time.