They wouldn't need to come here if we hadn't destroyed their countries. Do you think they want to leave the place their ancestors lived in for generations, usually walking for 1000s of miles, to live a life of relative poverty in the US?
This will get you started, but is only the tip of the iceberg.
https://en.wikipedia.org/wiki/United_States_involvement_in_regime_change_in_Latin_America
https://en.wikipedia.org/wiki/Operation_Condor