Can a baby start teething at 3 months, or is that never seen?

Yes. Most infants start teething between 4-8 months of age. There is a very wide range of what is "normal". I have seen several infants born with bottom front teeth already and many who didn't get their first tooth till 9-14 months old. In almost all cases it just works it own way out as the child grows.
Teething. I go back & forth on whether teething is a real process or one we invented to explain the fussiness of a non verbal infant.That said, some babies have teeth present at birth & some don't have teeth until ~ 15m.The hand to mouth, fist chewing, drooling, etc.Are more an expression of the joy they find in mouthing things than pain.I suppose they can teethe @ 3m if ever, but look for other pbms if fussy.
Possible. Although the milk teeth develop when the baby is growing in the womb, the teeth only start to grow throughout the gums when the baby is 6-9 months old (although it can be before or after these ages).
Yes. Teething at 3 months is normal. You can use teething rings and damp frozen wash clothes to help your child cope with the process of erupting the new teeth. Use the appropriate amount tylenol (acetaminophen) for severe teething pain. Avoid using medications that you rub on the gums b/c it only will last for 10 to 15 minutes and will not provide lasting relief.
Early. But not unheard of. Most children begin to get their first baby teeth (lower central incisors) at 6-9 months. Talk to your Pediatrician for advice as to how to sooth your child when he/she is teething. 1st Dental appointment should correspond with 1st b'day. Recommend that you see a Pediatric Dental Specialist, a Pedodontist, for all the same reasons you see a Pediatric Medical Specialist.