In "Story" mode you will be placed onto a street. Head to the right of the screen. Barriers force you into a shop. This is the first level of the game.
To pass this level head to the right, drift (release LT) around to the right to begin heading left again. Go past the swinging axe carefully and then let go of RT to begin drifting to the left. Head back towards the right and avoid the spring platforms to then drift to the right again (release LT). Head straight to the left and out the door to complete the first level.
You'll get the unlock notification on the result screen or once you hit continue at the latest.