What you want is called a 'biometric waiver' for Global Entry.

I know a 69-year-old who has one because her fingerprints could not be read-- they even called her in a month after the initial interview and did a standard FBI 10-card with ink to see if they could make that work. No dice. So now she uses the GE line, but cannot use the kiosk.

I assume a baby can also get a biometric waiver, at least for the first few years of life. They just didn't know (how) to do it.