Talk to your endo about it. Is he a specific paediatric endocrinologist?
I have Hashi's, and take levothyroxine every day. These are the guidelines for MY meds (which may well be different for a baby, but you need to explore it all i think since i don't know what form you've been given).
It must be taken on an empty stomach (the pill is supposed to get to the small intestine without being "digested" in the stomach for optimum absorption - washing it down with water upon waking and at least 30mins before food is how they advise adults/younger people to do it, but this is obviously not possible with a baby).
It must absolutely not be taken with a vitamin pill, an iron pill or anything with calcium in it (including milk) because it binds with some other minerals and will not get into the blood properly if that happens.
It should not be chewed, powdered or broken unless to adjust dose (25mcgm is the smallest pill readily available for adults, this will not be the case for newborns) - i'm not sure why.
As a person with hypothyroidism who has been on this medication for years i would give it to my newborn as i would a cat - i.e. i would put it far back on the tongue and then squirt a little liquid (of whatever sort was deemed ok - breastmilk or water or whatever) in on top then blow on the face to cause a swallow. I would then soothe and nurse immediately. I know this sounds cruel, and it certainly isn't the kindest way, but if no liquid form was available, knowing what i do (first hand from adult hypothyroidism and in reading about paediatric hypothyroidism) i would regard it as a necessary evil - child diabetics hate their injections, but it's too important to muck about with.
Hopefully your endo will be able to answer all of these questions. I too am a big supporter of the PKU test for this reason. Huge
to you, i know how daunted i felt when I was dx, i can't imagine having to deal with caring for a similarly affected newborn.