You need to draw eitr into your body, and the only way of doing that which we know of is to ingest edible items that have grown in the mist permeating from remains of jotun. It wouldn't make any sense to have magic fueled by that available earlier in the game.

Ymir's flesh could perhaps be used to similar extent, just as it is used to craft magical weapons like Frostner, but it would lie outside of the eitr system and thus not function as true magic as it is available in the game.

Furthermore, it's important for all players to learn the basics of battling in melee as well as when to rely on ranged attacks. Progression to magic instead of starting out with it is just fine.