You can actually get to the cupcake minigame without having to die over and over. For the PC version, in the Extras menu, put your mouse in the bottom left corner. An 8-Bit Baby sprite should appear. Click on it and you will play the minigame. For the Mobile version, the sprite is located on the right of the "Main Menu" text in the Extras menu.

(Thanks to CoolKoopa15 from GameFaqs for this guide)