Then fire him and get someone who can.
How do you prove someone is an illegal? You demand documents from him? He stands silently. Suppose this is done to you. You stand silently and get deported. Do you then sue?
Would you have the query performed only on Hispanic looking people?
If not, and you are asked to produce documents, would you do so? Would that not be an intrusion on your privacy? If an array of thousands choose to exercise their Constitutional right to remain silent and are deported, why should they not be able to sue? Are you prepared to pay the award from taxes?
What exactly is supposed to be the methodology for “if they are here illegally, get them out”?