The earliest in the season was probably the H2 hurricane that hit the northern Caribbean Islands on March 7, 1908. That same year on May 29th, a hurricane brushed Cape Hatteras, North Carolina. Probably the most unusual year was 1886 - on June 14th a hurricane hit far eastern Texas; on June 21st a Cat II hit the Florida panhandle; on June 30th another Cat II hit the Florida panhandle and on July 18th a hurricane hit north of Tampa. A hurricane hit the central Texas coast on June 28, 1929. A hurricane passed through the northern Bahamas on May 18, 1951. Hurricane Aubrey (Cat IV) hit the Texas/Louisiana border on June 27, 1957, and Hurricane Alma (Cat II) hit the Florida panhandle on June 9, 1966. There have been others since then and perhaps more prior to 1886 but that would take a fair piece of research.
Cheers,
ED