Testing is a great way to get a foot in the door!
I know a lot of people who think of it as "All I gotta do is test the game". I took a different approach and thought "What can I make of this and how can I stand out?" And so, if I found a bug, I would look through the scripts and suggest changes (as a tester NEVER demand a fix! Coders hate that). If I thought of a different/better way something could happen, I would suggest it to the design team. And in the little free time I had, I wrote a scenario with the help of one of the game's designers. As it happened, they loved the scenario so much it ended up being released with the game.
And ignore the size of the company. It happened at Firaxis, one of the biggest names in strategy.
Now I'm negotiating a contract to work on a new game, where I'll be the coder/designer.