This is simply untrue. Especially today, given the current systems and structures in place. The chances of significant social uplift for a child born into poverty in America is infinitesimal. Sure there are stories and instances of this happening, but the chances are probably similar to winning the lottery.
As an example, if all had the choice to "live where we please," wouldn't those who live in tornado alley choose to reside elsewhere? What about places considered to be "armpits of America" such as Buffalo, NY or Gary, IN or Nowheresville Coal Mining Town, WV? Do you think that everyone who still lives there wants to stay?
And moving to a different country altogether becomes even more problematic for lower income folk and those who live paycheck to paycheck.
FYI.
Peace!