Babies can eat mashed potatoes that are fully mashed and not chunky when the baby is around 4 to 6 months of age and eating solid foods.
Once your baby is able to eat solid foods such as baby food then you can begin feeding the baby mashed potatoes as long as you make sure the mashed potatoes are fully mashed up and has no chunks of potatoes in the mashed potatoes.
The chunks could cause choking for the baby but if the mashed potatoes are fully mashed the baby can safely eat them.
Some babies are ready to start solids as early as 4 months of age and others are not ready until around 6 or 7 months of age.