Great White sharks are not really uncommon in the GOM but they tend to be seasonal and most are juveniles. Most recent tracking data, from satellite-tagged fish, show a number come into the gulf late winter and into late spring(likely following the bluefin tuna migration and in much the same areas) then they leave, go around FL and back up the Atlantic coast to the NE. But, as with all apex predators, there are not many to begin with(compared to other shark species) and they usually aren’t right against the shore in the Gulf since we don’t have seals.
Comparatively, makos, a slightly smaller cousin and another member of the mackerel shark family, regularly come right up the beach in Spring following the first pushes of porpoises, cobia and jacks from S FL.