I am pretty much in the same position you're in. I recently relocated my business to a small city and expanded my seating, hours of operation, and menu.
As you know, most items purchased through distributors come in large quantities- 6 #10 cans/case. The problem in a small place is often having too much of something rather than too little. I should own stock in ziploc bags as I find I open a #10 can, use what I need for a recipe, and freeze the rest. Perishables are another story altogether!
I guess what I'm saying is that worse things can happen than running out of something. Naturally, you don't want to start out with half your menu 86'd, but having to sub cheddar for provolone won't turn customers off. You'll figure out the balance between ordering too much/having your $$ tied up in inventory and running out in no time at all. Until then, I'm sure there's a supermarket where you can grab a head of lettuce and a handful of tomatoes until you can get a delivery.
Good luck! I'd love to hear more about your cafe when you have time.