Is there a way to skip the tutorial?
No, there isn't. At the start of the game, only Hogsport, Lower Bullocks and Flottering are visible but the last two are not yet accessible. You must get 1 star in each one before unlocking the next.
Yes, it's a bit of a pain, but getting 1 star in Hogsport should take less than 10 minutes with fast-forward and prioritising light-headed patients in the GP queues.