The Union Army vessel "Fanny" launched a captive observation balloon to
observe Confederate positions near Hampton Roads on August 3, 1861 -
several months before the George Washington Parke Custis(1) became
operational. Plus the Fanny was a single screw steamship, not an
unpowered barge like the GWPC, which had to be towed.
If unmanned balloons count, the Austria Navy vessel "Vulcano" probably
deserves the accolades as the "first". Vulcano launched several
bomb-carrying hot air balloons towards Venice during the 1849 siege of
that city by the Austrians. A wind shift blew the bomb-laden balloons
back towards the Vulcano and the attempt was not repeated.
(1) Note the correct spelling is "Custis", not "Curtis" as is given in
the illustration caption.
Cheers,