Ancient peoples used trenches, but I don't think it would be described as "trench warfare". The Battle of Trench would be one obvious example, and the Arabic traditional sources describe it as having been proposed by a Persian, as the Persians supposedly used trenches as an anti-cavalry measure. Perhaps a Persianist can comment on whether or not that was the case, as the Arabic traditional sources can play a bit fast and lose with the historical record, to put it mildly. As far as I'm aware no one was actually inside these trenches in the style of WWI. They basically used it as a kind of dry moat to separate the two armies.

It's by no means my specialty, but I quite admire this video by Dr. Nicholas Murray about why WWI trench warfare developed in the particular way that it does and why it's different from previous uses of trench-like defenses like breastworks, and why specifically in WWI it was necessary to actually go underground into a trench. It certainly helped me to understand why you so suddenly see this defensive shift which doesn't really have much of an historical precedent.