Once nice thing about Google is the famed 20% time. If you have an idea, you're allowed to work on it roughly one day a week (or almost one week per month). You might hear some people say that it's a myth, or that it's too hard to actually use it. But if you can't manage to exercise a perk that everyone knows about, and that is sanctioned at the highest level, then it probably means you wouldn't have too much luck with your idea outside of Google either, IMO.