Hm... I'd prefer if the amount of zombies was lower at the beginning, and gradually rose up to the huge hordes there are now.
Also, possibly the ability to choose a small amount of starting equipment? You could have, say, 100 points at the start. Pants, shoes, and T-shirts would be free, but anything else would cost points. Your average pistol would be about 70-85 points to encourage searching, but it would be nice to at least be guaranteed that you could start out with some basic storage like a hoodie or messenger bag, or some basic supplies like books or nails. Possibly, you could also add perks which give equipment or companions. For example, you could be a beggar and start out with damaged clothes and less equipment, or you could be a "be prepared" kind of person and have better starting gear. Also, you might add an occupation you choose at the start that affects your skills and equipment. A librarian would have lots of books, a construction worker would have boards, nails, and a hammer, or a gangster would have lots of drugs and a few weapons. These jobs could affect how people react to you, for example, a survivor who was previously a cop would dislike theives and criminals, while a retired soldier would get along with a cop or hunter. Anyways, a complete autosave would also be nice too.
EDIT: I found how to escape the tutorial, but I have yet to make it out alive.
Here's how ya escape it:
Set the gasoline pump on fire, it will eventually burn down the wall. STAY THE HELL OUT OF THE SMOKE AND FIRE!