Enterprise NX-01 flies over the Gulf.
The Gulf of Mexico was a body of water on Earth. It was an extension of the Atlantic Ocean, bordered by North America.
Commander Charles Tucker III would often go swimming in the Gulf, sometimes inviting a girlfriend named Lisa. He would often tell T'Pol of his desire to show her some of the beaches of the Gulf. (ENT: "The Crossing")
In March of 2153, parts of the Gulf were attacked during the Xindi incident. (ENT: "The Expanse")
While discussing the prospect of leaving USS Voyager to live among a group of Humans settled in the Delta Quadrant, Chakotay reminded himself that he could never do it knowing that he would be giving up such prospects as seeing the sunrise over the Arizona desert, or swimming in the Gulf of Mexico on a summers day. (VOY: "The 37's")