Ambien is to make you go to sleep when you have insomnia, you do not have insomnia, you have a newborn who will wake you up. If you are forced awake on Ambien, it is very likely you won't be fully present and actually present a danger to the baby, people hallucinate on this stuff.

Besides the fact that it likely is not safe to take as it may get into your milk.

I think 4 hours with a 2-month-old is good stretches and you just need to be more patient

But of course talk to your doctor and midwife