I've done a bit of googling and the clear answer seems to be ww1 for cover against gunfire but more importantly cover from artillery.
I would imagine it wasn't used too far back due to inaccuracy of firearms but am just curious for solid answers instead of my uneducated speculation.
So I guess, when did they first become a prominent tactic and what changes in weaponry caused this tactic to be used?
The Cluilian trench was constructed outside of Rome as a defensive structure for an invading Army in the 7th century B.C. It must have worked pretty good because Roman armies adopted the building of trenches around their military encampments. Trenches were great for defense against an enemy phalanx (you would not believe how hard it is to maintain a shield wall while climbing into and out of a 2 meter deep trench) Also great for defending against cavalry (getting horses to jump a trench is not easy sure one or two might do it but it's probably not a great idea to be the guy on that one or two surrounded by 5,000 angry Romans). Not great for defending against archers but tents and shields can help you out there. The Cluilian trench is recorded by the Roman historian Livy.
Trenches continued to be used throughout history.
I think the first more modern use would probably be in the American Civil war. Just as you speculated it was for defense against improved artillery and firearms.
Additional to the first sentence of your question, an early record of the use of trenches as protection against firearms and artillery that preceeds both the American Civil War and the First World War was the Battle of Ohaeawai, New Zealand.
Elaborate trench and bunker systems were independently developed by the Maori, who successfully employed them as early as the 1840s to withstand British cannon, muskets, and an experimental poison-gas mortar, in the New Zealand Wars. British casualty rates of up to 45 percent, such as at the Battle of Ohaeawai in 1845, proved contemporary firepower was insufficient to dislodge defenders from a trench system.
Trenches, as far as we can tell, seem to have existed as far as organized warfare has. They were certainly not invented by the Romans, nor did they "fall out of favor" after Rome's passing. Even before firearms, trenches have been used as part of field fortifications. This isn't a very detailed answer, but there's not too much else to say in regards to your question.