Maerd: Well, Geralt was already an accomplished witcher when Kaer Morhen was destroyed and survived because he wasn't present during that event. What year was that? Nenneke could be 80 or even 90 years old, they don't tell her age and even in medieval times such long-living people existed.
She is not described as an old hag in this scene, I tell you that much. It`s 60 pusing it for sake of old-n-wise-Geralt thing.
Also, according to "History" by Roderic de November Kaer Morhen was sieged and destroyed in 1185-1188. But in 1264 Triss Merigold notes that school does not train new witchers for about quarter of century, meaning since about 1240.
Geralt, in my understanding, is a witcher of one of the last generations, but not the very last.
If he was born in 1210, than he must have hit the road in 1231 at age of 21 - age of adulthood in medieval times. And training at the fortress continued still.