Santa Cruz was founded on August 28, 1791 under the overall leadership of Fr. Fermin Lasuen, the second Father President of the mission chain. The founding missionaries (the men who were responsible for building the mission day-in and day-out in its initial years) were Fr. Isidro Salazar and Fr. Baldomero Lopez.
Fr. Salazar was born in the region of Cantabria, Spain. He served at Santa Cruz for about four years. Fr. Lopez served at Santa Cruz until mid-summer of 1796, when he returned to Mexico. Neither of these priests cared for "temporal administration" (the actual building and running of a large complex community) and they didn't get along too well.
Santa Cruz was not one of the most successful of the Spanish missions. Its highest recorded population was only 523, attained in 1796.