> The thought that a collection of gears can become aware of its existence seems, at least to me, pretty outlandish.

I mean, it's less exciting when you break that down into the what it means for a person to be aware of themselves. For me, it breaks down to neurons & symbols, well-known scientific domains. While I may not be right, it's not difficult to come up with plausible explanations for the phenomena humans experience. Most of the mystery comes from it being very difficult for most people to even define consciousness. Much of the syntax we have for it (in the west, at least) is cobbled together from various religions, spiritualities, and extremely, extremely dense philosophers read by few and understood by fewer.

You might find Richard Hofstadter's Book "I Am A Strange Loop" illuminating if you find my explanation meager.