It is not at all trivial to recognize a particular sound from its FFT spectrum. But it may be possible that particular frequencies will show up in a baby's cry and not in other sounds.
For what purpose?
It sounds like you're relatively new to audio analysis, to programming, and to this hardware. You've selected a very challenging early project. If you have a high tolerance for frustration and disappointment, then by all means, proceed. If not, you might be better advised to start with easier projects with hope of quicker success, and less rigorous theoretical demands.
I assume that you're using an Uno.
You'll need to characterize the sound you want to identify. I don't really know how you're going to get sample data from a baby crying. Maybe just run a recorder until you get what you want, or maybe introduce a recorder during the inevitable moments when somebody else unsuccessfully tries to quiet the baby. For heaven's sake, don't make it cry just to get audio samples.
You'll also need to characterize the ambient sound in the environment where you'll use it.
A baby's cry has a frequency of 3500kHz on average.