My son was born here too and we were given this advice that it's ok for babies or young children to be without visa but we had to face a lot of trouble while entering Thailand again after a short trip without him having a Non O visa.
He had to take a 15 days on arrival visa which was not extended and we had to leave the country and get a tourist visa for him which was then transferred to a Non O visa.
Do not leave until your son has a Non O visa or you can get him a tourist visa not the on arrival visa when you come back to Thailand. I hope this helps. (All this was last year)