Is it safe to give a baby OTC probiotics?

There is better. You can give your baby plain yogurt. That is better . In the past when there has been no formulas around they have been giving yogurt diluted with water. That is very good for the baby's digestion and yours.(much better than milk) that is called food is medicine ! use it. If you have time learn to prepare your own yogurt. That is going to be economical and fresh. Use organic full fat milk.