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No, you can't sue the military for allowing you to enlist. The Feres Doctrine prevents you from being able to sue the military at all, based on your service or decisions made by the government concerning your service.
On the issue of receiving disability benefits for your hearing loss, for you to receive it from the military you have to show that military service actually had something to do with your hearing loss. If you already had hearing loss when you joined and there is no evidence that anything about military service made your hearing loss worse, or the progression more severe, then there really isn't a legally viable VA claim against the military either.