If the baby is of teething age then yes the putting of their hands in their mouths can be a sign of teething.
Babies who are teething do put their fists or hands in their mouth and they tend to drool a lot or even cry when they have teething pain.
However babies do put their hands and fits in their mouths even when they are not teething but if they are of the age that teething happens then it can mean the baby is teething.
Some other signs of teething in babies are swollen or puffy gums and crying or fussing more often.
You can give the baby some rusks or teething biscuits if they are teething and old enough to have them or give them a teething ring or pacifier to help some.
Rusks are good for teething babies but it's recommended to only give it to them at 8 months of age or at least not until 6 months of age.
That is when they begin eating more solid, solid foods and be sure to always watch then closely when they are eating rusks or any other hard foods.
The earliest you can give a baby teething biscuits or other hard things such as crackers is 8 months of age.
Always supervise the baby when you do give them crackers or teething biscuits or whenever you feed them any food even when they can feed themselves.
Teething biscuits are also good for babies that are teething.
It's not advised to give a newly teething baby teething biscuits right away but wait until at least 8 months of age and then you can give them teething biscuits safely.
When your baby is between 4 to 6 months of age the baby can begin eating soft pureed foods and then as they get older and reach 8 months old or older they can eat other solid foods.
That includes the Gerber Puffs and other solid foods such as cereal, apples etc.
When they are little you should cut the foods up small enough so that they can easily chew it and not get choked on the food.
Always keep an eye on the baby and supervise them while eating foods even when they are feeding themselves.