OMG meeting your new baby has to be the most amazing experience any person could have! Just think, nobody can introduce you, because nobody has ever met this person before. It must be like being the first human on the moon.
Both dh and I were utterly overwhelmed by it.
It was particularly amazing for me with ds, our first child, as he was lifted on to my chest without my seeing his face or his genitals, so I didn't even know 'what' he was, and then I turned him over myself, and gazed into his face, and touched his hand, and explored him for a while before discovering for myself that he was XXX (we had two names ready). My heart is thumping just remembering that.
It was stunning the second time, too, with dd, but not quite so overwhelming, perhaps because I was told that she was a girl with dark hair before I ever saw her. But that feeling of intimate connection with someone nobody in the world has ever met before was just as extraordinary.