Eh, I gotta say I think you’re shooting yourself in the foot with this one. I’ve seen a lot of guides for writers recommend against the unnamed/genderless protagonist device. It’s not that this could not possibly be used well, but that it almost never is. It seems to be generally regarded as a show-off trick used by amateurs. See Points #6 and #18 here, for instance.
The only reasonable work-around I see is to make the story first-person. The baby wouldn’t know its own name and wouldn’t care what sex it is, so it’s natural that the subject wouldn’t arise. But if you want to write it in the third person, you’re going to be stuck either always saying “the baby did this” and “the baby did that” or calling the baby “it” all the time and sounding like a serial killer.
However, the Continental Op never was given a name, presumably the inspiration for Pronzini.
Le Guin has said that if she were writing Left Hand of Darkness today she wouldn’t use “he” as the standard pronoun. Since that time lots of sf writers have invented pronouns to use for ambiguous or alien sexes.
Any story not written from the standard first or third-person, past tense, has to be especially good to break through the barrier to the average reader. These are standard forms for good reason even though there are dozens of alternative ways to approach stories, all of which have been tried at times, some effectively and famously.
The best way to write this particular story is to use an ambiguous baby name. Markxxx, why isn’t that an option for you?