It's difficult to say definitively who was the *first* person to map the Texas coastline, as early exploration and mapping was often done by indigenous peoples before written records existed.

However, some of the earliest documented explorers who mapped parts of the Texas coastline include:

* Alonso Alvarez de Pineda: In 1519, he sailed the Gulf Coast from Florida to Mexico, charting the Texas coastline and identifying several bays and inlets.

* Francisco de Urdaneta: In 1539, he explored the coast of Texas and named the area "Panuco."

* Hernando de Soto: In 1542, he explored the interior of Texas and provided some information about the coastline.

* Luis de Moscoso Alvarado: After the death of De Soto, Moscoso led the surviving expedition members through Texas and explored the Gulf Coast.

It's important to note that these early maps were often inaccurate and incomplete. The first detailed and accurate map of the Texas coastline was likely created by René Robert Cavelier, Sieur de La Salle in the late 17th century. He established a settlement at Fort St. Louis near present-day Matagorda Bay and explored the coast extensively.

Therefore, while pinpointing the *absolute first* person to map the Texas coastline is challenging, these explorers played significant roles in early documentation of the area.