Cruz might have outlined it as you say, but Trump started using E-Verify when it first came out in 1996...where was Cruz then?
He served as Solicitor General of Texas from 2003 to 2008, appointed by Texas Attorney General Greg Abbott.
He was not involved with E-verify as he wasn’t employing people. Cruz is 25 years younger than Trump so it isn’t exactly relevant to compare what they were doing in 1996, is it?