When did Geralt get the scar on his face?

Stick with me here and this constructed order of events:

1. Ciri rescues Geralt from the Wild Hunt (not represented visually)

2. Geralt stumbles into the area around Kaer Morhen with no weapons and a big scar on this face (prologue to Witcher 1)

3. Ciri mentions that she's never seen the scar before and Geralt says he got it from a cockatrice. (Witcher 3)

When was Geralt supposed to fight that cockatrice?