Level doesn't have to be a purely-metagame element in the slightest, and can very well exist in the setting. All it needs is that some sort of in-setting training is required in order to level (which IMO should be the case anyway).
There's real-world examples* of "levels" all over the place, mostly to do with having to complete or fulfill one step in a training and-or experience+ process, and prove you have done so, before moving on to the next.
* - Grades 1 to 12 in school. Belt colours in martial arts. Apprentice-journeyman-master in trades. Loads of others.
+ - which experience points model beautifully!