But any one step along the way, since it does nothing by itself, could not give the organism that had it any competitive advantage. So why would each of those traits persist and prevail long enough for the complex system to fall into place?

In point of fact, evolution is a messy process, and any organism carries along a lot of useless genetic baggage. Fact is, unless a trait is actually harmful, there's no reason not to. Hell, my feet still have fingers. This baggage can manifest itself later, creating what may seem to be a very complex change in a short time. Birds still have dinosaur mojo somewhere in the deep recesses of their genetics, and human beings do to, down at the base of their brains.

The example often used for this kind of "impossible order" thinking is the eye, but closer examination shows that this isn't any more impossible to evolve than any other trait.

Remember, in natural selection and evolution, "good enough" works.