Early in his career, he moved to Venezuela due to the lack of opponents in his division.
There he received an opportunity for the Venezuelan Bantamweight championship, but lost by points to Hall of Famer Enrique Chaffardet.
Subsequently, he moved to New York and began boxing in other states, eventually capturing the Montreal Athletic Commission World Bantamweight Title.
In 1936, he defeated Tony Marino to unify this championship with the one recognized by the International Boxing Union, in the process becoming the third Latin American undisputed world boxing champion.
After retiring, he worked as a spokesperson for beer companies in New York, before returning to Puerto Rico in the 1960s, where he resided until his death.
He received several posthumous recognitions and his name was used in several sports venues and buildings.
In 2002, Escobar was inducted into the International Boxing Hall of Fame.