We are planning USA-FRA-BUD in the coming weeks. Two adults (vaccinated) and a three-year old, all on EU passports. German government regs exempt 6-year olds from tests and all. For adults it's either a test or vaccination certificate.
I did a Timatic check just to verify. If I put Germany as destination than "This does not apply to passengers under the age of 6" shows up. But if I put Germany as transit country with Hungary as destination, then the under 6 year old exemption does not show up. This is obviously a mistake in Timatic, but that's what the check-in agents will see. What should we do in this situation? It's actually hard to find a testing site that does tests for small children. All the travel testing services have a minimum age around 5-6.

Any thoughts, should we arrive at the airport days before departure and be prepared for endless back and forth until they check the actual government regs?

EDIT: Does it help if we are flying Lufthansa who should be more familiar with the rules? (Don't have the ticket yet, trying to score a last minute mileage ticket)