Cordina of Wales was first to compete for the Lionhearts and delivered performance to defeated opponent Eric Fowler 48-47 on all three of the judges' scorecards.
Liverpool's Fowler followed his compatriot in style as he claimed a second round knockout over Marquis Moore.
Fowler knocked down his opponent twice in round two before finishing him with an overhand right to mark an impressive first outing in the WSB and make it 2-0.
At light-heavyweight, the USA scored their sole victory when USA Knockouts' Kennedy Katende defeated British Lionhearts' Zlatko Ledic on points to make it 2-1.
However, that was the best it would get for the American franchise as Britain's heavyweight Fa claimed a unanimous win over Avery Gibson to settle the match before bantamweight McGoldrick, the Delhi 2010 Commonwealth Games champion, rounded things off in style with a split decision win over Braulio Avila Juarez.
"It was a very good night for the team," said Lee Pullen of British Lionhearts coaching team.
"The boxers adapted superbly to the different demands of World Series Boxing and we were very happy with their performances and the result."
The dominant win away from home will certainly send an early warning to Britain's rivals in the WSB, which is currently the only boxing competition in the world that allows fighters to box professionally but retain their Olympic eligibility.
The next fixture for the British Lionhearts is against Italia Thunder at the Celtic Manor Resort in Newport next Friday (November 23).
The bout will see the British Lionhearts boosted by the presence of London 2012 silver medallists Fred Evans of Wales and John Joe Nevin of Ireland, two of the franchises' biggest stars.
In addition Andrew Selby of Wales, who is the number one ranked amateur flyweight in the world, will also be in action.
Contact the writer of this story at firstname.lastname@example.org
November 2012: Nevin decides to stay amateur after signing with British WSB franchise
November 2012: British Lionhearts join AIBA's World Series of Boxing minus London 2012 champions
November 2012: Exclusive: - Britain to unveil World Series of Boxing franchise
September 2012: Joshua being lined up to lead British World Series of Boxing franchise
May 2012: Exclusive - British franchise being lined up to join World Series of Boxing