Originally NY 2 crossed the Hudson River on the Troy-Menands Bridge, which is now part of NY 378, and then turned south along NY 32, terminating at State Street in downtown Albany.
Around 1970, NY 2 was truncated at the intersection of 15th Street and Congress Street in Troy. This is at roughly the same time that I 787 was completed to the current NY 378 and the Menands/Menands Bridge Road access to the west end of the Troy-Menands Bridge was completely reconstructed into its current form.
Originally the east end of NY 378 headed straight down the hill on Menands Road, terminating where it met Broadway. You can see the gate blocking access from the current highway to the old road when heading down the hill eastbound on NY 378. During the construction of I 787 around 1970-71, the current routing was put in place.