The crisis caused by the US training low-level offenders into hardened criminals in its laughably misnamed “correctional” systems and then deporting them to Central American countries where they become prime actors in the destabilization of those countries which produces a refugee crisis impacting Mexico as well as the US?

No, not really, both because of the absence of a legal basis for any such suit, and because it wouldn't be targeting the responsible actor.

The one created by the violence from gangs using American guns?

The one created by the illegal drug demands of Americans?