I'm often asked by hopeful parents if those first precious smiles are real or just gas. That question makes sense. Around the same time as the peak of the fussy period (which will not last forever!), most babies start to have a real, joyful, social smile. 
From the start, babies are clearly tuned in socially. Even when they later start to become fascinated with their own hands, staring at them as they slowly turn them over, the human face remains more fascinating than anything else. This is especially true of their parents’ faces.

Babies can already recognize their parents on video and determine if the voice and video are just a bit out of synch. They also tend to respond differently when they see their mothers (comforted and calm) and when they see their fathers (perky and playful). (When they see strangers, they often go from bright-eyed to bored). They react to the moods of the people they are around.
When your baby was a newborn, the primary way of getting your attention was to cry. Soon, your baby learns to try to get your attention with gurgles, coos, and body movements. Then she is learns to reward you with a genuine smile when you connect in a way that brings her delight. You can recognize these smiles because the cheeks rise (called a Duchenne smile) or the mouth opens (an open-mouth smile); in moments of sheer joy, the mouth opens and the cheeks rise.
Smiles may not be frequent yet, but once you’ve experienced your baby smiling at you, you will be motivated to learn all the ways you can make her do it again. And she will be busy learning how to make you smile.
Yes, there is fussiness in the early weeks and months, but this is also a beautiful time of learning how to connect through a range of emotions and expressions. You can relax and enjoy, that real smile isn't gas and there are many more in your future.