Does it really have to be that complicated?
Step 1: Figure out what countries the 545 children who were stolen from their parents come from, which is presumably where their parents were deported.
Step 2: Run an advertising campaign in each of those countries inviting the parents to inform the U.S. embassy that their children were stolen.
Step 3: Give every parent who steps forward a genetic test to see if it matches any of the kids.
Step 4: For any match, the parents get their children back and a generous compensation package, including Stephen Miller's personal cell phone number.
(kidding about those last 7 words)
I'm sure that won't reunite all of the kids with their parents. No doubt a lot of these parents who had their kids ripped from their arms by agents of the U.S. government might be hesitant to contact the U.S. embassy for anything. The local foreign governments could be the go-between between the families and the U.S. if that makes things easier. If done right, it could find the parents for at least some, if not most, of these kids.
