WoTv2 says that magical talent usually surfaces during puberty.
However, usually does not mean always. Here are all the ages mentioned for characters that I’ve gathered:
Jowan came into his magic at age 5 or 6
Connor came into his magic at about age 12
Merrill came into her magic at age 4
Anders came into his magic at age 12
Emile de Launcet came into his magic at age 6
Talwyn came into his magic at age 10
Lysas came into his magic at age 9
Cole (the human Cole) came into his magic at about age 12
Rhys came into his magic at age 11
Fiona came into her magic at age 14
Velanna’s came into her magic at age 9
Vivienne says to Cassandra that she was taken to the Circle of Ostwick when she was very young, too young to remember her parents
Amell/Surana has the option to say they don’t remember where they’re from, to which the elven NPC will respond that they must have been taken when they were very young
So based on all this, it seems it’s far more accurate to say that magic most often develops in late childhood rather than teenage years, but sometimes children come into it barely out ofinfancy.