I thought they were available sooner than that
American 1600 lb AP bombs - yes.
British 1600 lb AP bombs - winter of 1943/44? Quote from Wiki entry about Op Tungsten, April 3rd 1944:
While carrier aircraft had previously lacked a bomb capable of penetrating a battleship's thick deck armour, it was hoped that the recently developed 1,600-pound (730 kg) armour-piercing bomb would be able to pierce at least the first layer of Tirpitz's armour if they were dropped from an altitude of 3,500 feet (1,100 m) or higher.