Not everyone was born to be an innovator or inventor ... the question is, can anyone learn?
In 2013, Time ran an interesting poll on the subject. It talks about reasons people invent, whether the qualities necessary are trainable, and the barriers to invention in many places.
via TIME
Like most things, I believe there's a mix of nature and nurture in inventiveness and innovation.
Some people are simply smarter (or more curious) than others. But that, in-and-of-itself, isn't enough to make them rich or successful (or prone to use those talents for innovation). Many factors combine to shape a person and their destiny. Examples include their natural abilities, environment (including their parents, location in time and place, and access to the time and space necessary to invent), and the practical realities of their situation.
Government policy also influences the behavior of its citizens and industry. Policy significantly impacts access to talent, resources, opportunities, and protection. These are things that the U.S. does well.
We're currently in the most inventive period of history ... and that's a staggering thought.
Luckily, I think it will only continue to grow as technology enables more.