There are no land giveaways anymore. The land you’re talking about is owned by Americans using it to feed & cloth the world.
You really haven't been to West Texas. :-)
With our crop yields getting higher and higher, the federal government is paying billions to farmer to not plant their fields (reducing the supply, and propping up the price).
My ancestors came to the US before it was the US, back in the 1600's and 1700's. Fortunately, it was before the occupants at that time said "No, we are full". The United States is still a long way from being "full".
Our problem is not lack of resources. It's the willingness to give cash and services to anyone that can make it inside the border. Even living in abject poverty in the US is an order of magnitude better than from where they came. That's what has to change: remove the incentive for someone to move here, just to go on public assistance.