Generally speaking, that should be able to be done in under sixty minutes, in front of a lay-magistrate or justice-of-the-peace.
The ICE agent(s) bring the "suspect" to such a magistrate, the magistrate does his thing, then non-citizens are returned to ICE.
The ICE agent takes the now-confirmed Illegal Alien to a Deportation Staging Center, with a rubber-stamped Deportation Order.
Pro formal lip-service as Due Process to satisfy the LETTER of The Law as we boot their nasty a$$e$ back to their own countries.