If valid, then it is fairly quick (seconds/minutes).

E-Verify is intended to give results in a few seconds.

Is it a *unique* SSN number not used by anyone else?

The check is if the name and SSN and birthdate all match the SSA's records.

Prior employment using that SSN?

That is not checked. It provides no information. People change jobs all the time.

Migrants do not usually have a SSN, they would have a work visa

If you are a foreigner authorized to work in the US, you will get a SSN. You also get a separate ID number (a USCIS A-Number or a Form I-94 Admission number). That number is required to be included on the I-9 the employee gives to the employer, and is included in the E-Verify information. I would hazard a guess that info is sent to Homeland Security rather than SSA to check that the individual is still authorized to work in the US.

TINs are reserved for foreigners who do not work in the US but have US source income and need to pay US income taxes. They are issued by the IRS, not the SSA.

I think the big thing you are missing in all of this is that the "Guillermo" I referred to in an earlier post is a guy who has gathered info on valid name/SSA/birthdate combos. That is fairly easily done if you know how to navigate the dark web. He is the guy who can comb through his list of valid combos to find and name and birthdate suitable to the person needing one. He might also provide (or know a separate source) to get a good quality fake ID or other info needed to "prove" identity.

Employers are easily tacit accomplices in this, in that they are only required to attest that they examined the identification presented. They are not required to retain copies. They can accept fake IDs without any liability on their part. (If they choose to keep copies of the ID, they must do so for all employees, not just selected employees.)

--Peter