Newborns are actually probably the best way to test the randomness theory. No newborn has a criminal record or any questionable history that would result in them needing extra scrutiny. If, however, they share name and/or DOB with someone who is a "bad guy", then the system could automatically put them in the extra scrutiny line.
Does your newborn have an extremely common name? If so, my guess is that increases your chances of him/her taking a long time to process.