Can I read book number three, Abaddon's Gate, from the series The Expanse by James S.A. Corey, without having read any of the previous books in the series?
You should read the novels in order. You'll have a MUCH better sense of what's going on and enjoy the books more, plus later books definitely contain spoilers re earlier ones.
There are a few very short novellas and short stories that don't need to be read to enjoy the novels.
You'll lose the background history/politics, but the base storyline of each book is fairly self contained. You'll also lose the introduction of the Protomolecule and Miller's backstory.
If you want an overview of the other books without having to read them, just take a look on the Wikipedia pages for a brief synopsis.