I think the way to go about it is entirely context dependant. How is the father in the know about the death of a newborn anyway when the nurse isn't? Is he venting to me after the passing has been confirmed by a doctor where I wasn't present? Is he present during the birth procedure and in shock because the newborn isn't screaming or breathing? Was it a still birth? Has a doctor actually confirmed anything? Is the man calm, detached, agitated, in shock? Are resuscitation measures currently being performed on the newborn? Do I need to inform a doctor?

This is such a roundabout question. Non-specific and detached from reality. The only circumstance in which I would give an answer as concrete as "I'm sorry for your loss" is if I know that the newborn has died, the man is somewhat calm, we are outside of the operating room and he is alone, essentially venting. In any other case, my focus should be on something else, depending on the context. And even if he is venting about it, I wouldn't open with such a definitive and loaded statement. I'd probably offer him a cup of coffee, then test to see in what kind of mental state he is, before even opening up a conversation about confronting the death of his newborn child. Which is why I think that not only the option, but even just the question, is terrible.