Well, let’s see... When Santa Anna declared himself dictator of Mexico, quite a few of the Mexican states immediately seceded from the Mexican Federation. Santa Anna overthrew all of these except TEXAS which thrashed him and remained an independent nation.
Meanwhile, the USA and CANADA are about to go to fist city over the Oregon Territories.
Enter the most powerful nation in the world, GREAT BRITAIN who controls Canada, and who recognizes TEXAS as a nation with the Rio Grande as the southern border.
Britain proposes a treaty between GB, Canada, Texas and Mexico against the USA.
This so horrified the Texans they immediately demanded statehood with the USA which is granted and the US rushes troops to the Rio Grande, the border recognized by Britain.
Mexico is not happy and begins their plans for reconquest, and fails.
The US recognizes the “back door” to the USA is open from the West, so they make Mexico a deal they could not refuse. In exchange for GOLD, Mexico gives up all claim to the western regions of the USA. Later they give even more gold for the Gadsden Purchase.
The Oregon question sorts itself out and the USA retains it.
So we did steal the land!