This timeline sets Jon Snow's age at 13 in the year 295 AC, making him 15 at the start of the canon story. This is slightly older than his book counterpart.
Jon Snow's Starting Age: 15
Robb Stark's Starting Age: ~15
Daenerys Targaryen's Starting Age: ~14
Part I: The Awakening & Departure (Pre-Story Events)
281 AC:The Tourney at Harrenhal. Rhaegar Targaryen crowns Lyanna Stark the Queen of Love and Beauty.
282 AC: Lyanna is "abducted" by Rhaegar. Robert's Rebellion begins. Jon Snow is born at the Tower of Joy to Lyanna Stark and Rhaegar Targaryen.
283 AC: The Rebellion ends. Daenerys Targaryen is born on Dragonstone.
289 AC: The Grejoy Rebellion begins and is crushed.
295 AC:[AU EVENT] At age 13, after a near-death experience in the Wolfswood, Jon Snow awakens the System, which he comes to call the 'Creed'. He begins secretly training.