First, it is important that we make the distinction between true drakes and common drakes.
Ryan Mercury was the first drake to awaken, in 2057
From shadowrun's wiki:
Drakes first came into the public awareness in the 2060s but appear to have been around prior to that in the Sixth World. It is said that in the Fourth World they were servants created by the dragons for dragons. At some point, drakes became capable of carrying on their traits to offspring.
Considering that last comment, i would say that common drakes have been around since magic returned, but they have been hiding since they are "free" from any dragon's control (unlike true drakes). Now, the person who is recognized as the first drake is not one of the true drakes from 4th era (earthdawn's setting), but a human who awakened as a drake after obtaining an artifact from a true dragon.
Ryan Mercury (aka Quicksilver) is a human turned into a drake that has been around since before the death of Dunkelzahn (August 9, 2057), but awakened when he obtained the dragon heart, which contains D's life force. In the trilogy, it is revealed that he was supposed to be a drake since the start, and that the artifact simply awakened his powers.
PS: There is more info about him on the Dragon Heart trilogy and the Clutch of Dragons 4th edition sourcebook.
After that, other common drakes began to awaken when the planet's mana levels rose again, in 2061 and 2062. Which match the appearance of SURGE awakened metacreatures aswell.