Humans sustained themselves just fine with out oil. A better question is how will we sustained ourselves without oil. Modern society will face much more challenges in a life without oil.
Our reliance on a global economy made possible by cheap energy has allowed us to concentrate populations and build infrastructures that are completely unsustainable when we no longer have cheap liquid fuel to transport foods from areas of high production to areas of high population. We will need a complete restructure of our societies, eating local will be come a necessity instead of a catchy phrase.
We have no alternative energy source that will prevent this. Over time we will all have to live simpler liver relying on less and less energy.