That's a good point. There is no Tumbler, no Bat, and no Batsuits in the cave. The biggest mystery of the film is what became of the Bat-pod (I'd like to think Selina rode it through that tunnel and went as far as she could before Bruce tracked her down via the necklace
So we know that Bruce's most dangerous machines are not there, and also I think the fact that there are no Bat-suits shows that Blake would definitely have to do more of his own thing if he were to fully adopt the superhero thing.
But as is, he could very well just be the world's greatest Private Investigator with the help of the Bat-computer. It's pretty open to interpretation what becomes of Blake.