Sucking is an inborn reflex for babies. It's perfectly natural for a newborn to suckle his fist, which also naturally leads to thumb sucking as he grows. Sucking calms your baby down. There are some advantages though: Your newborn will have a built-in way to calm himself down anytime he's feeling cranky, with no help needed from Mum. In this instance, it's either your baby's thumb or a pacifier that will calm him down. However, you need to take note that long-term thumb sucking or prolonged use of pacifier can disturb the alignment of your child's teeth and even the structure of his mouth. So you will definitely want to wean him off before his permanent front teeth come in. Most kids stop thumb sucking on their own by the time they're four. You can help your child wean off his thumb sucking by offering some other comfort objects (like a beloved stuffed animal or pillow) when he reaches for his thumb.
It’s a natural reflex for a baby to suck on the thumb or fists to find his own comfort. Some babies suck thumbs or fists even when they are inside mums’ womb. He usually stops on his own when he starts school though sometimes it’s a habit that hard to break. We can work with the child to reduce the dependency on thumb/fist sucking 1. Try to distract your baby by engaging both hands to play with toys. 2. Plan some activity that will stimulate him to think whether they want to suck the thumb or fists any longer. 3. Try to limit the time to suck like during bed time and explain to baby it is bed activity. 4. Praise and recognize him when he is not sucking on the thumb or fists. 5. As this is the comfort zone for the child, do not use ‘tricks’ to force him to stop sucking thumbs/fists. 6. Communicate with him to gain his understanding.
It depends how old is your baby. For babies, they will be wearing mittens, so if your baby loves to suckle his fists with the mittens on, it might not be so good for him as he will be suckling his mittens instead! Sucking is natural to baby. For me, i let him grab my fingers whenever i see him sucking his fists, or pull his hands away from his mouth. For older babies like teething time, use a chilled teething ring will help.