I thought the USA bought the land both of the Rio Grande for cash (gold) from Mexico so they could pay their enormous debts off.
This purchase, and the Louisiana Purchase under Jefferson, and buying Alaska from Russia, are the main components of how we legally built the land base of the USA.
The US paid around 15 to 18 million dollars....but this was for ‘damages’ and debt that the Mexican gov’t owed to Americans (one assumes for property purchased).