Starting sippy cups

When and how did you start introducing a sippy cup to your baby? Is 6 months too soon? My son will be 6 months next week, and refuses to hold his bottle but loves to hold a sippy cup with handles. I’ve only ever tried to give him water in a sippy cup (as recommended by his doctor for constipation). He’s formula fed, would it be okay to give him formula in a sippy cup? I’m a FTM and have no clue what I’m doing 😅 thanks in advance for any tips or advice.