No one likes to lose progress when playing video games, especially in action RPGs such as Anthem.
The good news is that with it being online-focused, Anthem has a robust autosave system in place. Basically, whenever you do anything noteworthy in its world, such as harvest components or complete a mission, the game saves. For the most part, then, you can rest assured that you can quit the game at any time and not lose any real progress.
Be aware though, that if you quit the game during a mission, any progress in that mission won’t be saved. You’ll have to start the mission from the beginning the next time you play. So, if you don’t want to lose any mission progress, complete it before you turn off the game.
When you do plan on quitting Anthem, it’s always a good idea to do so by entering the game’s menu, heading over to the settings tab, and then selecting quit to the main menu. That way, you can be sure that your progress has been saved. If you just exit the game by closing it down, there’s a small chance that you might lose a bit of progress.