Where was it even stated that one needed an activated Sharingan to use Susanoo?
The special chakra had already sprouted in Madara's brain and since Susanoo, unlike Amaterasu and Tsukuyomi, doesn't require eye contact with the victim, I see no reason Madara shouldn't be able to use it even without eye sockets.
And as far as I know, further Sharingan stages not only give access to new abilities, but also reduce their chakra cost and body exhaustion. So considering that Itachi was almost dead back then, activating his Sharingan was essential not to die from the lack of chakra when using Susanoo, though he probably could've done it just as Madara without Sharingan - if he had enough chakra.
I know that it may look like an asspull, but actually, I'm not really hating it that much given that so far manga hasn't given us any reason to think using Susanoo without Sharingan wasn't doable.