Doom Eternal's first DLC expansion, The Ancient Gods, will be less of an add-on and more of a stand-alone game when it releases, and you won't even have to own a copy of Doom Eternal to download and play it.
id Software's Marty Stratton confirmed to PCGamesN that the new DLC would be released as a standalone title rather than an add-on to the existing game, stating that the team "want the DLC to reach as many people as possible."
As such you can pick up and play the game even if you don't own Doom Eternal, although you'll probably want to do so anyway, given the two stories are intertwined. The DLC will follow on directly from the main story, and as it turns out, that final encounter as the ultimate apex predator has caused a little damage to, well, the entire universe.
The game's director, Hugo Martin, claimed that The Ancient Gods is more like "Doom Eternal Part Two" than a smaller DLC release and that fans should expect something "every bit as grand as the main game was."