From the time my baby was born, I was amazed at how well he could lift his head up. Only for a few seconds, at first, and it was never very steady, but even from the very beginning, that little smoosh of a nose would graze my cheek as he wobbled his head up and down and side to side (sometimes even with the surprise of an open mouth kiss on my face).
With the help of the much-despised tummy time, he got stronger and stronger. I actually think that the fierceness of the tummy time hatred (the crying, the throwing of the shoulders) helped strengthen those neck and back muscles even faster. I will never understand why babies are so against lying on their tummies...I would think that the new perspective would be a welcome change. But, what do I know? I'm just the woman forcing the issue.
The stronger those neck and back muscles got, though, the longer he would be able to hold his head up, and the less wobbling would occur. He even got to where he could raise his head and look around, which was a completely new and exciting occurrence. It was especially thrilling from the height of someone's shoulder as he was carried around, because he could then see the walls from many feet up in the air, or down to the ground that he spent so much time on.
Eventually, the wobble was completely gone and my baby was the one with the control and the power to hold and move his head exactly where he wanted it, so he could see what he wanted to see. It also became much easier to hold him, without the threat of an accidental head butt to the cheekbone.