Sucking is a completely normal need that infants have. Many even suck their thumbs before they're born—you might have seen your baby doing that on an ultrasound during pregnancy.
The sucking reflex is usually strongest in the baby's first year of life. A strong sucking reflex helps your baby make sure she gets the nutrition she needs from the breast or bottle. Sucking provides your baby comfort and helps her calm herself, especially when falling asleep. She also explores her hands and objects by putting them in her mouth to see how they feel and taste. If your baby's cutting her first teeth, so may use her fists to rub her sore gums.
Although you might not like the way pacifiers or thumbs look in your baby's mouth, remember that she probably won't use either for too long. Many babies give up sucking their hands or pacifiers by 6 to 7 months, and most children give it up by 2 to 4 years. Thumbsucking usually doesn't cause any harm unless it continues beyond 4 to 5 years, when it can affect the shape of your child's jaw or teeth as the permanent teeth are coming in.
Of course, it's important to wash your baby's hands frequently to reduce the chance that germs on her hands get into her mouth. Similarly, a pacifier is not usually harmful as long as you keep it clean, it's made of one piece to prevent choking on detachable parts, and you never tie it around your baby's neck because she can strangle on it.
The main advantage of the thumb is that your baby always has it available when she needs it to calm herself. The pacifier's main advantage is that you can take it away when you think she no longer needs it. But just remember that your baby is likely to stop sucking on her fist, thumb, fingers or pacifier within a few months after her sucking need lessens and she starts exploring more interesting things in her environment.
Our parenting advice is given as suggestions only. We recommend you also consult your healthcare provider, and urge you to contact them immediately if your question is urgent or about a medical condition.