Hey,
People are evaluated based on lot of factors which portfolio and personal statement are the most important ones.
I am studying film production at Chapman University and I know lot of people who don't have background in film and film industry.
But I encourage you to build your creative portfolio as much as possible and I am sure you will be admitted to your desired University. The only trick is producing fruitful work in short amount time rather than waiting few months to make something amazing instead (Though I encourage that too, but, you have to be sure that you are going to make something really amazing, which rarely happens when the person has minimum experience).
The good thing is that you don't have to necessarily ONLY produce films and short films back to back. It is good to have wide gamut of experience in different things when you are not producing films (from writing, directing, ... and writing short stories or doing management roles in different industries).