Here's a brief overview of all the films that Matt Damon had been involved in before 'Saving Private Ryan; 'Good Will Hunting', 'Chasing Amy', 'The Rainmaker', 'Mystic Pizza', and 'Courage Under Fire'. Despite that, prior to that chance meeting through Robin Williams, Spielberg had never seen or heard of the actor before. We guess we now know a lot more about Spielberg's own viewing habits!
The fact that he didn't know who Damon was actually appealed to Spielberg, though. He wanted a fresh face for his film; having cast Tom Hanks in the leading role he wanted the rest of the actors to be fairly anonymous so that they didn't become distracting. In his own way, he believed he was giving Damon his big break. That may not quite be true, but it's still a pretty cool story.