Preschool worker here:
He could be trying to find out what kind of security they have. Obviously, they are pretty suspicious, because they are not missing a child. If they were-- if even if a child who wasn’t expected that day was missing from home-- they would know, and what they would do, would be to get the police who would probably be there to talk to the guy, find his location, and go to him. If there were no police there, they would try to get his location themselves, and send the police there.
If they would happen to say “Oh, bring the kid over,” that’s already a security risk. But that still doesn’t get him into the building. It does get him to the parking lot, though, without sending up an alarm. Security is REALLY tight in preschools and daycare centers now. We check IDs of people we don’t immediately recognize against a list of people authorized to pick up a particular child, and we don’t let people into the building who don’t have business there, and can’t readily demonstrate their business. We are located in another business, so we do have people come to the wrong door, and we have to send them to the right door. So far, no one has argued, but if anyone did, it would send up red flags.
He might be planning on doing something like coming to the door with a backpack, and saying the kid was in the car, and asking if someone recognized the backpack, just to try to gain access to the building. It wouldn’t work. Like I said, letting the guy come to the school was already a bad move, but whoever went to the door would want to go to the car and see the child. That would be a bad move too-- don’t go anywhere with this guy-- but at least it risks just one employee, and not the whole school, which could be at risk if he were let in.
I don’t know why he wants access. He may not know where his kids are after a messy divorce, and his ex has a TRO, and so he wants to check out any place they may be. He may be looking for an ex-wife or girlfriend who is a teacher. He may just want to stir up trouble somewhere, and gaining access to a well-guarded preschool is a good “challenge.” Maybe he’s a potential shooter, looking for an easy mark.