Career
In 1629 Alpoim was appointed Alcalde de la hermandad. In 1632 he had received important Indian encomiendas, by the Viceroy of Peru Luis Jerónimo de Cabrera. He had also received a "encomienda" in Ylaty (Corrientes) composed of Guarani Indians.
In 1636 he bought in Potosí the title of Alférez realium
In 1646 Alpoim is elected as Alcalde of Buenos Aires. In 1647 Alpoim is appointed Lieutenant Governor of Santa Fé.
In Corrientes Province, he held the position of Lieutenant Governor in (1630, 1646, 1647-1648). In 1636 the General Amador Báez de Alpoim, led expeditions against the Indian serranos (inhabitants of sierra de Tandil), who attacked the tribes pampas (inhabited the plain).
His family had arrived in 1599, in the expedition of Diego Rodriguez de Valdéz.
The luxurious house had a Turret overlooking the coast. They had several children, including Juan Báez de Alpoim. Amador Báez de Alpoim by paternal line was descendant of French noblemen, and by maternal of the Kings of Portugal.