Final answer:
The new goal for the Spanish in New Mexico after Oñate left was establishing a permanent settlement and converting the indigenous people to Catholicism, as exemplified by the founding of Santa Fe.
Step-by-step explanation:
After Juan de Oñate left New Mexico, the new goal for the Spanish was to focus on establishing a permanent presence through colonization and religious conversion of indigenous peoples, rather than the search for gold and silver. This shift in objectives was represented by the founding of Santa Fe in 1610 as the capital of the Kingdom of New Mexico and the efforts of Franciscan missionaries to convert the Pueblo to Catholicism.
The hope of finding precious metals faded as it became clear that the region did not yield the wealth the Spanish had anticipated. Instead, the focus turned to creating a sustainable colonial society.
Through the establishment of missions and the spread of Catholicism, the Spanish aimed for a spiritual conquest alongside their colonial expansion. However, their efforts faced significant resistance, such as during the Pueblo Revolt in 1680, demonstrating the complexity of Spanish colonial ambitions and the resistance of indigenous peoples to cultural and religious imposition.