Hurricane season in the Atlantic is from June 1st to November 30th, and peaks during the second week of September. In the Pacific along the Americas it begins on May 15th. A storm must first reach above 39 mph to be classified a Tropical Storm and get named. Just getting a system to form means that the water is roughly 80F among other conditions. The historical significance of this helps different areas to prepare or plan for certain times of the year. See the historical origin maps and videos tracking the record 2005 season.
The maps in this slide show below break down the locations for tropical storm formation. Each map represents a 10-day period with historical plots for development. This begins on May 10th, almost a month before the typical season begins. Every eight to nine years a storm does form in May, with 18 identified on these maps. If it were to happen, the Caribbean Sea would be the ‘most likely’ spot to look.
Historical time of the formation of tropical storms and where this occurred. Data for the Atlantic starts from 1851, Pacific in 1949. Source: NOAA, National Hurricane Center