Photo of the Day: Mission San Xavier del Bac in Tucson, Ariz. Todd DeFeo 10 years ago Mission San Xavier del Bac was built between 1783-1797 in what was then New Spain. An absolutely magnificent example of Spanish Colonial architecture. (Photo by Todd DeFeo) TUCSON, Ariz. — Mission San Xavier del Bac was built between 1783-1797 in what was then New Spain.