If you find a barbarian encampment, consider farming it for experience. This is a particularly effective strategy in Civ VI because:
- As Martinus said, there doesn't seem to be an XP cap for killing barbarians
- The gold reward for taking it isn't really that impressive
- Barbarians are more of a nuisance in Civ VI but once you find the encampment it's pretty easy to neutralize the threat. Just station an archer by the encampment (or a warrior and slinger) to watch the camp and the mischief is managed.
With any luck, you'll have an early army all with 1 or 2 levels of experience.