It's only a problem if (1) the immigrants in question behaving in a dangerous and criminal fashion, or (2) you need to urgently deport millions of peaceful, non-dangerous immigrants in an extremely short period of time, and you don't care about the harm this does to society.
Obviously in case (1) you can just detain and carefully identify people, since they're actually doing dangerous things and you'll have probable cause to detain them. Note that this was the case that nearly all the 2024 election rhetoric was focused on (i.e., deporting the "rapists and murders".)
In practice we're seeing that the true goal is (2), rapid emergency deportation and arrest of non-criminal immigrants. There is absolutely no emergency that requires this to be done quickly or carelessly, such that there's any risk to US citizens' (or immigrants) civil rights. It can be done carefully, with strong evidence, without violating civil rights. But of course, violating civil rights and creating disorder appears to be the goal.