You are thinking to big. Look for a niche. If there are 2 dozen startups already competing in that space, it's not very niche.
There are plenty of opportunities out there big enough to make a founder very wealthy, but not big enough to attract the least bit of interest from a VC.
Consumables. The big players are brain dead in terms of product innovation which means you get successful small companies entering all the time. Greek yogurt, deodorant, energy bars (Hi! I'm the cofounder of Mealsquares!), coffee, you name it. Tech founders don't want to touch this stuff.
That's because those things are flooded with competitors and margins don't scale nearly as well as pure tech. Every time I walk through my local farmers market I see a new brand of Kumbucha or Flat Tummy Tea.
But, there is competition everywhere, and it gets fiercer by the day. So pick something you're truly interested in and roll with it until the wheels fall off. That's really your only chance ( if you have one at all ).
There are plenty of opportunities out there big enough to make a founder very wealthy, but not big enough to attract the least bit of interest from a VC.