I introduced solids with DS1 just before he was 6 months old (baby led weaning) and introduced the sippy cup with water at the same time.
To him, it was just another thing to play with on his high chair tray. He would lift it up, chew on it, wave it around and throw it on the floor constantly (
) He didn't start taking any decent amount of water from it until about 10 months of age.
So at 4 months, I would not be in a rush to introduce the cup just for the sake of it.