1. The Spanish did not "steal" the land from the Aztecs and other people groups from Tierra del Fuego to central California?
2. As can be seen in the Treaty of Guadalupe Hidalgo,
https://www.archives.gov/milestone-documents/treaty-of-guadalupe-hidalgo , Articles XII-XV, the US paid 15 million in gold or silver, with 6% per annum interest and assumed some $3M in debts owed by Mexico to US citizens. Depending on how quickly the US paid off the $12M remaining after the initial immediate $3M payment, the US may have paid as much as $20M-$25M for what is now the SW US. At the time the Treaty was negotiated and signed, the discovery of gold at Sutter's mill was unknown to the negotiators. The resources and potential of all that land was largely unknown.