After the cutscene, press the B button to jump off the wall.
Run outside and talk to Toad so he asks you to rescue Peach again.
Try to leave, and Toad will stop you and tell you to save.
Ignore him and leave and head left back to Bowser's Keep, then mash A through the cutscene with Exor.
Return to Mario's Pad, run inside the house and talk to Toad again.
Follow Toad out of the house and try to leave the area. When he bumps back into you, pick the second option both times to skip the tutorials about using items and timed hits.
Finally leave the area and head to Mushroom Way.