After immigrants are detained by ICE, there are probably records somewhere of who has an attorney, and who is calling family members or an attorney.
For the immigrants who aren't calling any family or lawyers, the poorest of the poor, people with little to no connection to anyone, who may not even say which country they are from, if the administration were actually trying to kill as many disconnected immigrants as possible in secret, would society know?
For example, if the administration was composed of all types of conservative people, but 30 percent were secretly Nazis or wanted racial genocide, could there be a campaign to not just remove, but kill, immigrants, and the public doesn't find out?
It's not just the SS, the Wehrmacht also "suffered" from having to shoot all these people. Read up on Babij Jar, Ukraine. Even Himmler is on record expressing sympathy for his killers. That's why the bullet based plan turns into a gas based one. Because it's "easier" to flip a switch on a room full of people than to shoot naked people to fall on other corpses already in the ditch.