How far could someone get leaving the country with a child they can’t prove is theirs?

I’m sorry with how this question is worded lol. I’m writing a story where the MC gets kidnapped and flown out of his home country. The criminal gets him a boarding pass as his child and off they go.

The criminal slips up and get caught somehow by being unable to provide real or convincing documents that the MC is his, leading to his arrest and the MC being placed somewhere and unable to go back to his home country. MC is basically a John Doe and too young to really remember his parents or where he lived at first, so he’s stuck there.

It’s a story with supernatural/sci-fi/occult elements so the criminal doesn’t really care about putting the MC into school and would rather experiment on him. Is there a plausible way I can get the criminal caught? What requires a “parent” to show identification for their child?