The Atlantic hurricane season normally gets off to a slow start and ramps up through the summer months, peaking around September 10th.
Activity is typically low in June and on average, there's one June named storm in the Atlantic, Caribbean or Gulf of Mexico every one to two years. However there have been exceptions, with tropical storms Bonnie, Colin and Danielle in the Atlantic basin in 2016 and Bret and Cindy in 2017. Hurricanes are even rarer in June with about one hurricane every five years.
Atmospheric conditions are often unfavorable for tropical development over the central and eastern Atlantic during June due to the dry Saharan Dust Layer which sweeps off the coast of Africa and moves across the Atlantic. Also, disburbances moving off of Africa tend to be weak and do not develop into tropical systems.
The more common areas for development in June are along the southeast U.S. coast, the Gulf of Mexico and the western Caribbean. This is where sea surface temperatures are usually higher, compared to the Atlantic basin. Any storms that do form typically track north or northeastward, which brings the Gulf Coast and the Southeast coast in play for potential impacts.
However, there have been major impacts in June due to tropical storms. Tropical Storm Allison in 2001 made landfall as a weak tropical storm near Freeport, Texas and quickly weakened but the remnants lingered for days causing severe flooding in the Houston area.