Eisenhower did it.
https://thefederalistpapers.org/us/how-eisenhower-dealt-with-americas-first-illegal-crisis
"‘Ike’ took quick and decisive action. He used 1,075 Border Patrol Agents to seal the border. In doing so, he achieved a task our government today deems impossible with a force that is 10% larger. Once the border was sealed, Eisenhower went about the process of removing the millions of illegal aliens.
In June of 1954, he appointed retired General Joseph “Jumpin’ Joe” Swing to head “Operation Wetback,” which sent local and federal officials on sweeps of Mexican neighborhoods looking for illegals.
Within one month 50,000 illegals had been captured and deported, while nearly half a million more fled the country to avoid arrest. By September 80,000 more illegals had been removed from the state of Texas alone, and between 500,000-700,000 more had fled the country.
These illegals weren’t just dropped at the border; Swing arranged for buses and trains to take immigrants deep into Mexico before releasing them. Tens of thousands more were shipped by boat from Texas to Vera Cruz, Mexico."