By Ali Hibbs Albany, N.Y. — The second span of the Kosciuszko Bridge will open to traffic before rush hour early on Thursday morning, carrying commuters from Queens into Brooklyn four years ahead of schedule. The Kosciuszko Bridge, the first new major bridge crossing constructed in New York City since the Verrazzano Bridge in 1964, will be also opened to the public on Wednesday from noon to 6 p.m.