Indexing varchar column to search for first letter
I'm not sure what DBMS you are using but in general yes.  It looks like your index is doing what it is supposed to.  As a general case the optimizers can take advantage of an index in a "like" query if there are no pattern (_%[] etc) characters on the left hand side.

So this will use an index

oggetto.titolo like 'C%'


But this could not

oggetto.titolo like '%C'