i dont know...do Aeris got healing materia? cause if she does thats allowed. but yeah, only limits and healing here and there...sometimes in the game you start out different places with full health. so the trick is to lvl as much as possible, as close to death as possible to have higj lvl to get far in shinra HQ.
I do not think it is possible to complete shinra. Cause of the boss for nanaki. but found items are allowed so maybe.

i wish i just posted this challenge many years ago, when the game was still new. Cause im not a good enough gamer to even know if it is possible to get out of midgard like this.
I myself got up some floors but i think it stopped when i had to fight those guards at some elevator