I believe it's impossible, as you'll always become the 2nd driver on the team. (Correct me if I'm wrong.)
I was correct, but still wrong. You can become the first driver, but the previous first driver, will become the second driver. So if we take Redbull as an example:
First season at Redbull;
First driver: S. Vettel
Second driver: [Player]
Second season at Redbull:
First driver: [Player]
Second driver: S. Vettel
I hope it makes sense.