Sure thing - after university I got a job at one of the many dot.com startups that venture capitalists were hurling money at circa 2000 (before the bubble burst). The company was called HaHaBonk and it made comedy content for broadband before most people had broadband (we were the future, but the future kept dragging its heels). I worked as a content editor and general dogsbody, but the guys running it were generous about spotting opportunities for their staff, and one of them put me in touch with a co-producer on the MAGIC ROUNDABOUT movie which, with my then-partner, I ended up doing some rewriting work on.
Off the back of that an agent, a contact via my then-girlfriend (now wife), offered to represent us. I probably got an easier break than if I'd known nobody, but the bottom line was still having work of (reasonable) quality to present to someone when an opportunity arose. I think that's always the bottom line with writers: the way in is to write a great, great script. Contacts alone can't give you a career, they can only introduce you to people who won't like your mediocre work; on the other hand, people are usually generous - excited, too - to help promote a new and talented voice irrespective of that writer's background.