Since the accepted answer does not mention Mexico, I can add an observation here. The modern nation-state's immediate predecessor was the Viceroyalty of New Spain (and later that of New Galicia). Spanish monarchs' investments in discovery and exploitation were more important for their colonization project than any legislation (but note the issuance of extensive Laws of the Indies). New Spain attained its maximum extent around 1800 with possessions in Florida; thereafter it, and its successor Mexico, gradually lost territory to the United States through the Adams-Onís Treaty, Texas's brief independence, and the Mexican-American War.
Mexico's territorial expansion occurred during the colonial period, so it is Spain to which we should look for analogues to Manifest Destiny. The mother country, a Catholic state with great influence over Rome, could represent itself to be doing God's work (while conveniently extracting huge profits). Ecclesiastical sanction for Spain's domination of the New World was acquired in the Treaty of Tordesillas. In light of this document, the colonizers' successful invasions and systemic racism once in power, and their technical and biological advantages, it seems clear that Spain believed it deserved to dominate the Americas.